path: root/noise.md

---
title:      'The Noise Protocol Framework'
author:     'Trevor Perrin (noise@trevp.net)'
revision:   '34draft'
status: 'official/unstable'
date:       '2018-07-01'
bibliography: 'my.bib'
link-citations: 'true'
---

# 1. Introduction

Noise is a framework for crypto protocols based on Diffie-Hellman key
agreement.  Noise can describe protocols that consist of a single message as
well as interactive protocols.  

# 2. Overview

## 2.1. Terminology

A Noise protocol begins with two parties exchanging **handshake messages**.
During this **handshake phase** the parties exchange DH public keys and perform
a sequence of DH operations, hashing the DH results into a shared secret key.
After the handshake phase each party can use this shared key to send encrypted
**transport messages**.

The Noise framework supports handshakes where each party has a long-term
**static key pair** and/or an **ephemeral key pair**.  A Noise handshake is
described by a simple language.  This language consists of **tokens** which are
arranged into **message patterns**.  Message patterns are arranged into
**handshake patterns**.

A **message pattern** is a sequence of tokens that specifies the DH public keys
that comprise a handshake message, and the DH operations that are performed
when sending or receiving that message.  A **handshake pattern** specifies the
sequential exchange of messages that comprise a handshake.

A handshake pattern can be instantiated by **DH functions**, **cipher
functions**, and **hash functions** to give a concrete **Noise protocol**.

## 2.2. Overview of handshake state machine

The core of Noise is a set of variables maintained by each party during a
handshake, and rules for sending and receiving handshake messages by
sequentially processing the tokens from a message pattern.

Each party maintains the following variables:

 * **`s, e`**: The local party's static and ephemeral key pairs (which may be
   empty).

 * **`rs, re`**: The remote party's static and ephemeral public keys (which may
   be empty).

 * **`h`**: A **handshake hash** value that hashes all the handshake data that's
   been sent and received.

 * **`ck`**: A **chaining key** that hashes all previous DH outputs.  Once the
   handshake completes, the chaining key will be used to derive the encryption
   keys for transport messages.
 
 * **`k, n`**: An encryption key `k` (which may be empty) and a counter-based
   nonce `n`.  Whenever a new DH output causes a new `ck` to be calculated, a
   new `k` is also calculated.  The key `k` and nonce `n` are used to encrypt
   static public keys and handshake payloads.  Encryption with `k` uses some
   **AEAD** cipher mode (in the sense of Rogaway [@Rogaway:2002]) 
   and uses the current `h` value as **associated data**
   which is covered by the AEAD authentication.  Encryption of static public
   keys and payloads provides some confidentiality and key confirmation during
   the handshake phase.

A handshake message consists of some DH public keys followed by a **payload**.
The payload may contain certificates or other data chosen by the application.
To send a handshake message, the sender specifies the payload and sequentially
processes each token from a message pattern.  The possible tokens are:

 * **`"e"`**: The sender generates a new ephemeral key pair and stores it in
   the `e` variable, writes the ephemeral public key as cleartext into the
   message buffer, and hashes the public key along with the old `h` to derive a
   new `h`.

 * **`"s"`**: The sender writes its static public key from the `s` variable
   into the message buffer, encrypting it if `k` is non-empty, and hashes the
   output along with the old `h` to derive a new `h`.

 * **`"ee", "se", "es", "ss"`**: A DH is performed between the initiator's key
   pair (whether static or ephemeral is determined by the first letter) and the
   responder's key pair (whether static or ephemeral is determined by the
   second letter).  The result is hashed along with the old `ck` to derive a
   new `ck` and `k`, and `n` is set to zero.

After processing the final token in a handshake message, the sender then writes
the payload into the message buffer, encrypting it if `k` is non-empty, and
hashes the output along with the old `h` to derive a new `h`.

As a simple example, an unauthenticated DH handshake is described by the
handshake pattern:

      -> e
      <- e, ee

The **initiator** sends the first message, which is simply an ephemeral public key.
The **responder** sends back its own ephemeral public key.  Then a DH is performed
and the output is hashed into a shared secret key.

Note that a cleartext payload is sent in the first message, after the cleartext
ephemeral public key, and an encrypted payload is sent in the response message,
after the cleartext ephemeral public key.  The application may send whatever
payloads it wants.

The responder can send its static public key (under encryption) and
authenticate itself via a slightly different pattern:

      -> e
      <- e, ee, s, es

In this case, the final `ck` and `k` values are a hash of both DH results.
Since the `es` token indicates a DH between the initiator's ephemeral key and
the responder's static key, successful decryption by the initiator of the
second message's payload serves to authenticate the responder to the initiator.

Note that the second message's payload may contain a zero-length plaintext, but
the payload ciphertext will still contain authentication data (such as an
authentication tag or "synthetic IV"), since encryption is with an AEAD mode.
The second message's payload can also be used to deliver certificates for the
responder's static public key.

The initiator can send *its* static public key (under encryption), and
authenticate itself, using a handshake pattern with one additional message:

      -> e
      <- e, ee, s, es
      -> s, se

The following sections flesh out the details, and add some complications.
However, the core of Noise is this simple system of variables, tokens, and
processing rules, which allow concise expression of a range of protocols.

# 3.  Message format

All Noise messages are less than or equal to 65535 bytes in length.
Restricting message size has several advantages:

 * Simpler testing, since it's easy to test the maximum sizes.

 * Reduces the likelihood of errors in memory handling, or integer overflow. 

 * Enables support for streaming decryption and random-access decryption of
   large data streams.

 * Enables higher-level protocols that encapsulate Noise messages to use an efficient
 standard length field of 16 bits.

All Noise messages can be processed without parsing, since there are no type or
length fields.  Of course, Noise messages might be encapsulated within a
higher-level protocol that contains type and length information.  Noise
messages might encapsulate payloads that require parsing of some sort, but
payloads are handled by the application, not by Noise.

A Noise **transport message** is simply an AEAD ciphertext that is less than or
equal to 65535 bytes in length, and that consists of an encrypted payload plus
16 bytes of authentication data.  The details depend on the AEAD cipher
function, e.g. AES256-GCM, or ChaCha20-Poly1305, but typically the
authentication data is either a 16-byte authentication tag appended to the
ciphertext, or a 16-byte synthetic IV prepended to the ciphertext.

A Noise **handshake message** is also less than or equal to 65535 bytes.  It
begins with a sequence of one or more DH public keys, as determined by its
message pattern.  Following the public keys will be a single payload which can
be used to convey certificates or other handshake data, but can also contain a
zero-length plaintext.

Static public keys and payloads will be in cleartext if they are sent in a
handshake prior to a DH operation, and will be AEAD ciphertexts if they occur
after a DH operation.  (If Noise is being used with pre-shared symmetric keys,
this rule is different; see [Section 9](#pre-shared-symmetric-keys)).  Like transport messages, AEAD
ciphertexts will expand each encrypted field (whether static public key or
payload) by 16 bytes.

For an example, consider the handshake pattern:

      -> e
      <- e, ee, s, es
      -> s, se

The first message consists of a cleartext public key (`"e"`) followed by a
cleartext payload (remember that a payload is implicit at the end of each
message pattern).  The second message consists of a cleartext public key
(`"e"`) followed by an encrypted public key (`"s"`) followed by an encrypted
payload.  The third message consists of an encrypted public key (`"s"`)
followed by an encrypted payload.  

Assuming each payload contains a zero-length plaintext, and DH public keys are
56 bytes, the message sizes will be:

  1. 56 bytes (one cleartext public key and a cleartext payload)
  2. 144 bytes (two public keys, the second encrypted, and encrypted payload)
  3. 88 bytes (one encrypted public key and encrypted payload)

&nbsp;
\newpage

# 4. Crypto functions

A Noise protocol is instantiated with a concrete set of **DH functions**,
**cipher functions**, and **hash functions**.  The signature for these
functions is defined below.  Some concrete functions are defined in [Section
12](#dh-functions-cipher-functions-and-hash-functions).

The following notation will be used in algorithm pseudocode:

 * The `||` operator concatenates byte sequences.
 * The `byte()` function constructs a single byte.

## 4.1. DH functions

Noise depends on the following **DH functions** (and an associated constant):

 * **`GENERATE_KEYPAIR()`**: Generates a new Diffie-Hellman key pair.  A DH key pair
   consists of `public_key` and `private_key` elements.  A `public_key`
   represents an encoding of a DH public key into a byte sequence of
   length `DHLEN`.  The `public_key` encoding details are specific to each set
   of DH functions.

 * **`DH(key_pair, public_key)`**: Performs a Diffie-Hellman calculation
   between the private key in `key_pair` and the `public_key` and returns an output
   sequence of bytes of length `DHLEN`.  For security, the Gap-DH problem based
   on this function must be unsolvable by any practical cryptanalytic adversary
   [@gapdh].  

     The `public_key` either encodes some value which is a generator in a large
     prime-order group (which value may have multiple equivalent encodings), or
     is an invalid value.  Implementations must handle invalid public keys
     either by returning some output which is purely a function of the public
     key and does not depend on the private key, or by signaling an error to
     the caller.  The DH function may define more specific rules for handling
     invalid values.

 * **`DHLEN`** = A constant specifying the size in bytes of public keys and DH
   outputs.  For security reasons, `DHLEN` must be 32 or greater.

## 4.2. Cipher functions

Noise depends on the following **cipher functions**:

 * **`ENCRYPT(k, n, ad, plaintext)`**: Encrypts `plaintext` using the cipher
   key `k` of 32 bytes and an 8-byte unsigned integer nonce `n` which must be
   unique for the key `k`.  Returns the ciphertext.  Encryption must be done
   with an "AEAD" encryption mode with the associated data `ad` (using the
   terminology from [@Rogaway:2002]) and returns a ciphertext that is the same
   size as the plaintext plus 16 bytes for authentication data.  The entire
   ciphertext must be indistinguishable from random if the key is secret (note
   that this is an additional requirement that isn't necessarily met by all
   AEAD schemes).

 * **`DECRYPT(k, n, ad, ciphertext)`**: Decrypts `ciphertext` using a cipher
   key `k` of 32 bytes, an 8-byte unsigned integer nonce `n`, and associated
   data `ad`.  Returns the plaintext, unless authentication fails, in which
   case an error is signaled to the caller.

 * **`REKEY(k)`**:  Returns a new 32-byte cipher key as a pseudorandom function
   of `k`.  If this function is not specifically defined for some set of cipher
   functions, then it defaults to returning the first 32 bytes from `ENCRYPT(k,
   maxnonce, zerolen, zeros)`, where `maxnonce` equals 2^64^-1, `zerolen` is a
   zero-length byte sequence, and `zeros` is a sequence of 32 bytes filled with
   zeros.

## 4.3. Hash functions

Noise depends on the following **hash function** (and associated constants):

 * **`HASH(data)`**: Hashes some arbitrary-length data with a
   collision-resistant cryptographic hash function and returns an output of
   `HASHLEN` bytes.

 * **`HASHLEN`** = A constant specifying the size in bytes of the hash output.
   Must be 32 or 64.

 * **`BLOCKLEN`** = A constant specifying the size in bytes that the hash
   function uses internally to divide its input for iterative processing.  This
   is needed to use the hash function with HMAC (`BLOCKLEN` is `B` in [@rfc2104]).

Noise defines additional functions based on the above `HASH()` function:

 * **`HMAC-HASH(key, data)`**:  Applies `HMAC` from [@rfc2104] 
   using the `HASH()` function.  This function is only called as part of `HKDF()`, below.

 * **`HKDF(chaining_key, input_key_material, num_outputs)`**:  Takes a `chaining_key` byte
   sequence of length `HASHLEN`, and an `input_key_material` byte sequence with 
   length either zero bytes, 32 bytes, or `DHLEN` bytes.  Returns a pair or triple of byte sequences each of length `HASHLEN`, depending on whether `num_outputs` is two or three:
     * Sets `temp_key = HMAC-HASH(chaining_key, input_key_material)`.
     * Sets `output1 = HMAC-HASH(temp_key, byte(0x01))`.
     * Sets `output2 = HMAC-HASH(temp_key, output1 || byte(0x02))`.
     * If `num_outputs == 2` then returns the pair `(output1, output2)`.
     * Sets `output3 = HMAC-HASH(temp_key, output2 || byte(0x03))`.
     * Returns the triple `(output1, output2, output3)`.

   Note that `temp_key`, `output1`, `output2`, and `output3` are all `HASHLEN` bytes in
   length.  Also note that the `HKDF()` function is simply `HKDF` from [@rfc5869] 
   with the `chaining_key` as HKDF `salt`, and zero-length HKDF `info`.

# 5. Processing rules

To precisely define the processing rules we adopt an object-oriented
terminology, and present three "objects" which encapsulate state variables and
contain functions which implement processing logic.  These three objects are
presented as a hierarchy: each higher-layer object includes one instance of the
object beneath it.  From lowest-layer to highest, the objects are:

 * A **`CipherState`** object contains `k` and `n` variables, which it uses to
   encrypt and decrypt ciphertexts.  During the handshake phase each party has
   a single `CipherState`, but during the transport phase each party has two
   `CipherState` objects: one for sending, and one for receiving.

 * A **`SymmetricState`** object contains a `CipherState` plus `ck` and `h`
   variables.  It is so-named because it encapsulates all the "symmetric
   crypto" used by Noise.  During the handshake phase each party has a single
   `SymmetricState`, which can be deleted once the handshake is finished.

 * A **`HandshakeState`** object contains a `SymmetricState` plus DH variables
   `(s, e, rs, re)` and a variable representing the handshake pattern.
   During the handshake phase each party has a single `HandshakeState`, which
   can be deleted once the handshake is finished.

To execute a Noise protocol you `Initialize()` a `HandshakeState`.  During
initialization you specify the handshake pattern, any local key pairs, and any
public keys for the remote party you have knowledge of.  After `Initialize()`
you call `WriteMessage()` and `ReadMessage()` on the `HandshakeState` to
process each handshake message.  If any error is signaled by the `DECRYPT()` or
`DH()` functions then the handshake has failed and the `HandshakeState` is deleted.

Processing the final handshake message returns two `CipherState` objects, the
first for encrypting transport messages from initiator to responder, and the
second for messages in the other direction.  At that point the `HandshakeState`
should be deleted except for the hash value `h`, which may be used for post-handshake channel binding (see [Section 11.2](#channel-binding)).

Transport messages are then encrypted and decrypted by calling
`EncryptWithAd()` and `DecryptWithAd()` on the relevant `CipherState` with
zero-length associated data.  If `DecryptWithAd()` signals an error due to
`DECRYPT()` failure, then the input message is discarded.  The application may
choose to delete the `CipherState` and terminate the session on such an error,
or may continue to attempt communications.  If `EncryptWithAd()` or
`DecryptWithAd()` signal an error due to nonce exhaustion, then the
application must delete the `CipherState` and terminate the session.

The below sections describe these objects in detail.

## 5.1. The `CipherState` object

A `CipherState` can encrypt and decrypt data based on its `k` and `n`
variables:

  * **`k`**: A cipher key of 32 bytes (which may be `empty`).  `Empty` is a
    special value which indicates `k` has not yet been initialized.

  * **`n`**: An 8-byte (64-bit) unsigned integer nonce.

A `CipherState` responds to the following functions.  The `++` post-increment
operator applied to `n` means "use the current `n` value, then increment it".
The maximum `n` value (2^64^-1) is reserved for other use.  If incrementing `n`
results in 2^64^-1, then any further `EncryptWithAd()` or `DecryptWithAd()`
calls will signal an error to the caller.

  * **`InitializeKey(key)`**:  Sets `k = key`.  Sets `n = 0`.

  * **`HasKey()`**: Returns true if `k` is non-empty, false otherwise.

  * **`SetNonce(nonce)`**: Sets `n = nonce`.  This function is used for
    handling out-of-order transport messages, as described in [Section 11.4](#out-of-order-transport-messages).  

  * **`EncryptWithAd(ad, plaintext)`**:  If `k` is non-empty returns
    `ENCRYPT(k, n++, ad, plaintext)`.  Otherwise returns `plaintext`.

  * **`DecryptWithAd(ad, ciphertext)`**:  If `k` is non-empty returns
    `DECRYPT(k, n++, ad, ciphertext)`.  Otherwise returns `ciphertext`.  If an
    authentication failure occurs in `DECRYPT()` then `n` is not incremented
    and an error is signaled to the caller.

  * **`Rekey()`**: Sets `k = REKEY(k)`.

## 5.2. The `SymmetricState` object

A `SymmetricState` object contains a `CipherState` plus the following
variables:

  * **`ck`**: A chaining key of `HASHLEN` bytes.
  * **`h`**: A hash output of `HASHLEN` bytes.

A `SymmetricState` responds to the following functions:   
 
  * **`InitializeSymmetric(protocol_name)`**:  Takes an arbitrary-length
   `protocol_name` byte sequence (see [Section 8](#protocol-names-and-modifiers)).  Executes the following steps:

      * If `protocol_name` is less than or equal to `HASHLEN` bytes in length,
        sets `h` equal to `protocol_name` with zero bytes appended to make
        `HASHLEN` bytes.  Otherwise sets `h = HASH(protocol_name)`.  

      * Sets `ck = h`. 

      * Calls `InitializeKey(empty)`.

  * **`MixKey(input_key_material)`**:  Executes the following steps:
  
      * Sets `ck, temp_k = HKDF(ck, input_key_material, 2)`.
      * If `HASHLEN` is 64, then truncates `temp_k` to 32 bytes.
      * Calls `InitializeKey(temp_k)`.

  * **`MixHash(data)`**:  Sets `h = HASH(h || data)`.

  * **`MixKeyAndHash(input_key_material)`**:  This function is used for
    handling pre-shared symmetric keys, as described in [Section
    9](#pre-shared-symmetric-keys). It executes the following steps:
  
      * Sets `ck, temp_h, temp_k = HKDF(ck, input_key_material, 3)`.
      * Calls `MixHash(temp_h)`.
      * If `HASHLEN` is 64, then truncates `temp_k` to 32 bytes.
      * Calls `InitializeKey(temp_k)`.

  * **`GetHandshakeHash()`**:  Returns `h`.  This function should only be
    called at the end of a handshake, i.e. after the `Split()` function has
    been called.  This function is used for channel binding, as described in
    [Section 11.2](#channel-binding) 

  * **`EncryptAndHash(plaintext)`**: Sets `ciphertext = EncryptWithAd(h,
    plaintext)`, calls `MixHash(ciphertext)`, and returns `ciphertext`.  Note that if 
    `k` is `empty`, the `EncryptWithAd()` call will set `ciphertext` equal to  `plaintext`.

  * **`DecryptAndHash(ciphertext)`**: Sets `plaintext = DecryptWithAd(h,
    ciphertext)`, calls `MixHash(ciphertext)`, and returns `plaintext`.  Note that if 
    `k` is `empty`, the `DecryptWithAd()` call will set `plaintext` equal to `ciphertext`. 

  * **`Split()`**:  Returns a pair of `CipherState` objects for encrypting
    transport messages.  Executes the following steps, where `zerolen` is a zero-length
    byte sequence:
      * Sets `temp_k1, temp_k2 = HKDF(ck, zerolen, 2)`.
      * If `HASHLEN` is 64, then truncates `temp_k1` and `temp_k2` to 32 bytes.
      * Creates two new `CipherState` objects `c1` and `c2`.
      * Calls `c1.InitializeKey(temp_k1)` and `c2.InitializeKey(temp_k2)`.
      * Returns the pair `(c1, c2)`.  


## 5.3. The `HandshakeState` object

A `HandshakeState` object contains a `SymmetricState` plus the following
variables, any of which may be `empty`.  `Empty` is a special value which
indicates the variable has not yet been initialized.
 
  * **`s`**: The local static key pair 
  * **`e`**: The local ephemeral key pair
  * **`rs`**: The remote party's static public key
  * **`re`**: The remote party's ephemeral public key 

A `HandshakeState` also has variables to track its role, and the remaining
portion of the handshake pattern:

  * **`initiator`**: A boolean indicating the initiator or responder role.

  * **`message_patterns`**: A sequence of message patterns.  Each message
    pattern is a sequence of tokens from the set `("e", "s", "ee", "es", "se",
    "ss")`.  (An additional `"psk"` token is introduced in [Section
    9](#pre-shared-symmetric-keys), but we defer its explanation until then.)

A `HandshakeState` responds to the following functions:

  * **`Initialize(handshake_pattern, initiator, prologue, s, e, rs, re)`**:
    Takes a valid `handshake_pattern` (see [Section 7](#handshake-patterns)) and an
    `initiator` boolean specifying this party's role as either initiator or
    responder.  
    
    Takes a `prologue` byte sequence which may be zero-length, or
    which may contain context information that both parties want to confirm is
    identical (see [Section 6](#prologue)).  
    
    Takes a set of DH key pairs `(s, e)` and
    public keys `(rs, re)` for initializing local variables, any of which may be empty.
    Public keys are only passed in if the `handshake_pattern` uses pre-messages 
    (see [Section 7](#handshake-patterns)).  The ephemeral values `(e, re)` are typically
    left empty, since they are created and exchanged during the handshake; but there are
    exceptions (see [Section 10](#compound-patterns)).

    Performs the following steps:

      * Derives a `protocol_name` byte sequence by combining the names for the
        handshake pattern and crypto functions, as specified in [Section
        8](#protocol-names-and-modifiers). Calls `InitializeSymmetric(protocol_name)`.

      * Calls `MixHash(prologue)`.

      * Sets the `initiator`, `s`, `e`, `rs`, and `re` variables to the
        corresponding arguments.

      * Calls `MixHash()` once for each public key listed in the pre-messages
        from `handshake_pattern`, with the specified public key as input (see
        [Section 7](#handshake-patterns) for an explanation of pre-messages).
        If both initiator and responder have pre-messages, the initiator's
        public keys are hashed first.  If multiple public keys are listed in
        either party's pre-message, the public keys are hashed in the order
        that they are listed.

      * Sets `message_patterns` to the message patterns from `handshake_pattern`.

  * **`WriteMessage(payload, message_buffer)`**: Takes a `payload` byte sequence
   which may be zero-length, and a `message_buffer` to write the output into.  Performs the following steps, aborting if any `EncryptAndHash()` call returns an error:
\newpage

      * Fetches and deletes the next message pattern from `message_patterns`,
        then sequentially processes each token from the message pattern:

          * For `"e"`:  Sets `e` (which must be empty) to `GENERATE_KEYPAIR()`.
            Appends `e.public_key` to the buffer.  Calls `MixHash(e.public_key)`.

          * For `"s"`:  Appends `EncryptAndHash(s.public_key)` to the buffer.  

          * For `"ee"`: Calls `MixKey(DH(e, re))`.

          * For `"es"`: Calls `MixKey(DH(e, rs))` if initiator, `MixKey(DH(s, re))` if responder.

          * For `"se"`: Calls `MixKey(DH(s, re))` if initiator, `MixKey(DH(e, rs))` if responder.

          * For `"ss"`: Calls `MixKey(DH(s, rs))`.

      * Appends `EncryptAndHash(payload)` to the buffer.  

      * If there are no more message patterns returns two new `CipherState`
        objects by calling `Split()`.

  * **`ReadMessage(message, payload_buffer)`**: Takes a byte sequence
    containing a Noise handshake message, and a `payload_buffer` to write the
    message's plaintext payload into.  Performs the following steps, aborting
    if any `DecryptAndHash()` call returns an error:

      * Fetches and deletes the next message pattern from `message_patterns`,
        then sequentially processes each token from the message pattern:

          * For `"e"`: Sets `re` (which must be empty) to the next `DHLEN`
            bytes from the message.  Calls `MixHash(re.public_key)`. 

          * For `"s"`: Sets `temp` to the next `DHLEN + 16` bytes of the message if
            `HasKey() == True`, or to the next `DHLEN` bytes otherwise.  Sets `rs` (which must be empty)
            to `DecryptAndHash(temp)`.

          * For `"ee"`: Calls `MixKey(DH(e, re))`.

          * For `"es"`: Calls `MixKey(DH(e, rs))` if initiator, `MixKey(DH(s, re))` if responder.

          * For `"se"`: Calls `MixKey(DH(s, re))` if initiator, `MixKey(DH(e, rs))` if responder.

          * For `"ss"`: Calls `MixKey(DH(s, rs))`.

      * Calls `DecryptAndHash()` on the remaining bytes of the message and stores
        the output into `payload_buffer`.

      * If there are no more message patterns returns two new `CipherState`
        objects by calling `Split()`.

# 6. Prologue 

Noise protocols have a **prologue** input which allows arbitrary data to be
hashed into the `h` variable.  If both parties do not provide identical
prologue data, the handshake will fail due to a decryption error.  This is
useful when the parties engaged in negotiation prior to the handshake and want
to ensure they share identical views of that negotiation.  

For example, suppose Bob communicates to Alice a list of Noise protocols that
he is willing to support.  Alice will then choose and execute a single
protocol.  To ensure that a "man-in-the-middle" did not edit Bob's list to
remove options, Alice and Bob could include the list as prologue data.

Note that while the parties confirm their prologues are identical, they don't
mix prologue data into encryption keys. If an input contains secret data that’s
intended to strengthen the encryption, a PSK handshake should be used
instead (see [Section 9](pre-shared-symmetric-keys)).  


# 7. Handshake patterns 

## 7.1. Handshake pattern basics

A **message pattern** is some sequence of tokens from the set `("e", "s", "ee",
"es", "se", "ss", "psk")`.  The handling of these tokens within
`WriteMessage()` and `ReadMessage()` has been described previously, except for
the `"psk"` token, which will be described in [Section
9](pre-shared-symmetric-keys).  Future specifications might introduce other
tokens.

A **pre-message pattern** is one of the following sequences of tokens:

  * `"e"`
  * `"s"`
  * `"e, s"`
  * empty


A **handshake pattern** consists of:

  * A pre-message pattern for the initiator, representing information about
  the initiator's public keys that is known to the responder.

  * A pre-message pattern for the responder, representing information about the
  responder's public keys that is known to the initiator.

  * A sequence of message patterns for the actual handshake messages.

The pre-messages represent an exchange of public keys that was somehow
performed prior to the handshake, so these public keys must be inputs to
`Initialize()` for the "recipient" of the pre-message.  

The first actual handshake message is sent from the initiator to the responder.
The next message is sent from the responder, the next from the initiator, and so
on in alternating fashion.


The following handshake pattern describes an unauthenticated DH handshake consisting of two message patterns:

    NN:
      -> e
      <- e, ee

In the following handshake pattern both the initiator and responder possess
static key pairs, and the handshake pattern comprises three message patterns:

    XX:
      -> e
      <- e, ee, s, es
      -> s, se

The handshake pattern names are `NN` and `XX`.  This naming convention will be
explained in [Section 7.4](#interactive-handshake-patterns).

Non-empty pre-messages are shown as pre-message patterns prior to the delimiter
`"..."`.  If both parties have a pre-message, the initiator's is listed first,
and hashed first.  During `Initialize()`, `MixHash()` is called on any
pre-message public keys, as described in [Section
5.3](#the-handshakestate-object).

The following handshake pattern describes a handshake where the initiator has
pre-knowledge of the responder's static public key and uses it for "zero-RTT"
encryption:

    NK:
      <- s
      ...
      -> e, es 
      <- e, ee

In the following handshake pattern both parties have pre-knowledge of the
other's static public key.  The initiator's pre-message is listed first:

    KK:
      -> s
      <- s
      ...
      -> e, es, ss
      <- e, ee, se

\newpage

## 7.2. Alice and Bob

In all handshake patterns shown previously, the initiator is the party on the
left (sending with right-pointing arrows) and the responder is the party on the
right.

However, multiple Noise protocols might be used within a **compound protocol**
where the responder in one Noise protocol becomes the initiator for a later
Noise protocol.  As a convenience for terminology and notation in this case, we
introduce the notion of **Alice** and **Bob** roles which are different from
initiator and responder roles.  Alice will be viewed as the party on the
left (sending messages with right arrows), and Bob will be the party on the
right.

Handshake patterns written in **canonical form** (i.e. **Alice-initiated
form**) assume the initiator is Alice (the left-most party).  All processing
rules and discussion so far have assumed canonical-form handshake patterns.

However, handshake patterns can be written in **Bob-initiated form** by
reversing the arrows and the DH tokens (e.g. replacing `"es"` with `"se"`, and
vice versa).  This doesn't change the handshake pattern, it simply makes it
easier to view Alice-initiated and Bob-initiated handshakes side-by-side.

Below are the handshake patterns from the previous section in Bob-initiated
form:

    NN:
      <- e
      -> e, ee

    XX:
      <- e
      -> e, ee, s, se
      <- s, es

    NK:
      -> s
      ...
      <- e, se
      -> e, ee

    KK:
      <- s
      -> s
      ...
      <- e, se, ss
      -> e, ee, es

For an example of Bob-initiated notation, see [Section
10.2](#the-fallback-modifier).

## 7.3. Handshake pattern validity 

Handshake patterns must be **valid** in the following senses:

 1. Parties can only perform DH between private keys and public
   keys they possess.

 2. Parties must not send their static public key or ephemeral public key more
    than once per handshake (i.e. including the pre-messages, there must be no
    more than one occurrence of `"e"`, and one occurrence of `"s"`, in the
    messages sent by any party).

 3. After performing a DH between a remote public key and any local private key
    that is not the ephemeral private key, the local party must not call
    `ENCRYPT()` unless it has also performed a DH between the ephemeral
    private key and the remote public key.  

Patterns failing the first check are obviously nonsense.

The second check outlaws redundant transmission of values to simplify
implementation and testing.

The third check is necessary because Noise uses DH outputs involving ephemeral
keys to randomize the shared secret keys, and to provide forward secrecy.
Patterns failing this check could result in subtle but catastrophic security
flaws.

Users are recommended to only use the handshake patterns listed below, or other
patterns that have been vetted by experts to satisfy the above checks.

## 7.3. One-way handshake patterns 

The following handshake patterns represent "one-way" handshakes supporting a
one-way stream of data from a sender to a recipient.  These patterns could be
used to encrypt files, database records, or other non-interactive data streams.

Following a one-way handshake the sender can send a stream of transport
messages, encrypting them using the first `CipherState` returned by `Split()`.
The second `CipherState` from `Split()` is discarded - the recipient must not
send any messages using it (as this would violate the rules in [Section 7.3](#handshake-pattern-validity)).

One-way patterns are named with a single character, which indicates the 
status of the sender's static key:

\newpage

 * **`N`** = **`N`**o static key for sender
 * **`K`** = Static key for sender **`K`**nown to recipient
 * **`X`** = Static key for sender **`X`**mitted ("transmitted") to recipient

+-------------------------+
|     N:                  |
|       <- s              |
|       ...               |
|       -> e, es          |
+-------------------------+
|     K:                  |
|       -> s              |
|       <- s              |
|       ...               |
|       -> e, es, ss      |
+-------------------------+
|     X:                  |
|       <- s              |
|       ...               |
|       -> e, es, s, ss   |
+-------------------------+

`N` is a conventional DH-based public-key encryption.  The other patterns
add sender authentication, where the sender's public key is either known to the
recipient beforehand (`K`) or transmitted under encryption (`X`).

\newpage

## 7.4. Interactive handshake patterns (fundamental)

The following handshake patterns represent interactive protocols.  These 
12 patterns are called the **fundamental** interactive handshake patterns.

The fundamental interactive patterns are named with two characters, which
indicate the status of the initiator and responder's static keys:

The first character refers to the initiator's static key:

 * **`N`** = **`N`**o static key for initiator
 * **`K`** = Static key for initiator **`K`**nown to responder
 * **`X`** = Static key for initiator **`X`**mitted ("transmitted") to responder
 * **`I`** = Static key for initiator **`I`**mmediately transmitted to responder,
 despite reduced or absent identity hiding

The second character refers to the responder's static key:

 * **`N`** = **`N`**o static key for responder
 * **`K`** = Static key for responder **`K`**nown to initiator
 * **`X`** = Static key for responder **`X`**mitted ("transmitted") to initiator

\newpage

+---------------------------+--------------------------------+
|     NN:                   |        KN:                     |
|       -> e                |          -> s                  |
|       <- e, ee            |          ...                   |
|                           |          -> e                  |
|                           |          <- e, ee, se          |
+---------------------------+--------------------------------+
|     NK:                   |        KK:                     |
|       <- s                |          -> s                  |
|       ...                 |          <- s                  |
|       -> e, es            |          ...                   |
|       <- e, ee            |          -> e, es, ss          |
|                           |          <- e, ee, se          |
+---------------------------+--------------------------------+
|     NX:                   |         KX:                    |
|       -> e                |           -> s                 |
|       <- e, ee, s, es     |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, se, s, es  |
+---------------------------+--------------------------------+
|     XN:                   |         IN:                    |
|       -> e                |           -> e, s              |
|       <- e, ee            |           <- e, ee, se         |
|       -> s, se            |                                |
+---------------------------+--------------------------------+
|     XK:                   |         IK:                    |
|       <- s                |           <- s                 |      
|       ...                 |           ...                  |
|       -> e, es            |           -> e, es, s, ss      |
|       <- e, ee            |           <- e, ee, se         |
|       -> s, se            |                                |
+---------------------------+--------------------------------+
|     XX:                   |         IX:                    |
|       -> e                |           -> e, s              |
|       <- e, ee, s, es     |           <- e, ee, se, s, es  |
|       -> s, se            |                                |
+---------------------------+--------------------------------+

\newpage

The `XX` pattern is the most generically useful, since it supports mutual
authentication and transmission of static public keys.

All fundamental patterns allow some encryption of handshake payloads:

 * Patterns where the initiator has pre-knowledge of the responder's static
   public key (i.e. patterns ending in `K`) allow **zero-RTT** encryption,
   meaning the initiator can encrypt the first handshake payload.  

 * All fundamental patterns allow **half-RTT** encryption of the first response
   payload, but the encryption only targets an initiator static public key in
   patterns starting with `K` or `I`.

The security properties for handshake payloads are usually weaker than the
final security properties achieved by transport payloads, so these early
encryptions must be used with caution.

In some patterns the security properties of transport payloads can also vary.
In particular: patterns starting with `K` or `I` have the caveat that the
responder is only guaranteed "weak" forward secrecy for the transport messages
it sends until it receives a transport message from the initiator.  After
receiving a transport message from the initiator, the responder becomes assured
of "strong" forward secrecy.

More analysis of these payload security properties is in [Section 7.6](#payload-security-properties).

## 7.5. Interactive handshake patterns (deferred)

The fundamental handshake patterns in the previous section perform DH operations for authentication (`"es"` and `"se"`) as early as possible.  

An additional set of handshake patterns can be described which defer these authentication DHs to the next message.  To name these **deferred handshake patterns**, the numeral "1" is used after the first and/or second character in a fundamental pattern name to indicate that the initiator and/or responder's authentication DH is deferred to the next message.

Deferred patterns might be useful for several reasons:

 * The initiator might have prior knowledge of the responder's static public key, but not wish to send any 0-RTT encrypted data.

 * In some cases, deferring authentication can improve the identity-hiding properties of the handshake (see [Section 7.7](#identity-hiding)). 

 * Future extensions to Noise might be capable of replacing DH operations with signatures or KEM ciphertexts, but would only be able to do so if the sender is authenticating themselves (signatures) or the sender is authenticating the recipient (KEM ciphertexts).  Thus every fundamental handshake pattern is only capable of having each authentication DH replaced with a signature *or* KEM ciphertext, but the deferred variants make both replacements possible.

Below are two examples showing a fundamental handshake pattern on the left, and deferred variant(s) on the right.  The full set of 23 deferred handshake patterns are in the [Appendix](#deferred-patterns).

+---------------------------+--------------------------------+
|     NK:                   |         NK1:                   |
|       <- s                |           <- s                 |
|       ...                 |           ...                  |
|       -> e, es            |           -> e                 |
|       <- e, ee            |           <- e, ee, es         |
|                           |                                |
+---------------------------+--------------------------------+
|     XX:                   |         X1X:                   |   
|       -> e                |           -> e                 |
|       <- e, ee, s, es     |           <- e, ee, s, es      |
|       -> s, se            |           -> s                 |
|                           |           <- se                |
|                           |                                |
|                           |         XX1:                   |
|                           |           -> e                 |
|                           |           <- e, ee, s          |
|                           |           -> es, s, se         |
|                           |                                |
|                           |         X1X1:                  |
|                           |           -> e                 |
|                           |           <- e, ee, s          |   
|                           |           -> es, s             |  
|                           |           <- se                |
|                           |                                |
+---------------------------+--------------------------------+




## 7.6. Payload security properties

The following table lists the security properties for Noise handshake and
transport payloads for all the one-way patterns in [Section 7.4](#one-way-handshake-patterns) and the fundamental patterns in 
[Section 7.5](#interactive-handshake-patterns).  Each payload is assigned a "source"
property regarding the degree of authentication of the sender provided to the
recipient, and a "destination" property regarding the degree of
confidentiality provided to the sender.

The source properties are:

 0. **No authentication.**  This payload may have been sent by any party,
    including an active attacker.

 1. **Sender authentication *vulnerable* to key-compromise impersonation
    (KCI)**.  The sender authentication is based on a static-static DH
    (`"ss"`) involving both parties' static key pairs.  If the recipient's
    long-term private key has been compromised, this authentication can be
    forged.  Note that a future version of Noise might include signatures,
    which could improve this security property, but brings other trade-offs.

 2. **Sender authentication *resistant* to key-compromise impersonation
    (KCI)**.  The sender authentication is based on an ephemeral-static DH
    (`"es"` or `"se"`) between the sender's static key pair and the
    recipient's ephemeral key pair.  Assuming the corresponding private keys 
    are secure, this authentication cannot be forged.

The destination properties are:

 0. **No confidentiality.**  This payload is sent in cleartext.

 1. **Encryption to an ephemeral recipient.**  This payload has forward
    secrecy, since encryption involves an ephemeral-ephemeral DH (`"ee"`).
    However, the sender has not authenticated the recipient, so this payload
    might be sent to any party, including an active attacker.

 2. **Encryption to a known recipient, forward secrecy for sender
    compromise only, vulnerable to replay.** This payload is encrypted based
    only on DHs involving the recipient's static key pair.  If the recipient's
    static private key is compromised, even at a later date, this payload can
    be decrypted.  This message can also be replayed, since there's no
    ephemeral contribution from the recipient.

 3. **Encryption to a known recipient, weak forward secrecy.**  This
    payload is encrypted based on an ephemeral-ephemeral DH and also an
    ephemeral-static DH involving the recipient's static key pair.  However,
    the binding between the recipient's alleged ephemeral public key and the
    recipient's static public key hasn't been verified by the sender, so the
    recipient's alleged ephemeral public key may have been forged by an active
    attacker.  In this case, the attacker could later compromise the
    recipient's static private key to decrypt the payload. Note that a future
    version of Noise might include signatures, which could improve this
    security property, but brings other trade-offs.

 4. **Encryption to a known recipient, weak forward secrecy if the
    sender's private key has been compromised.**  This payload is encrypted
    based on an ephemeral-ephemeral DH, and also based on an ephemeral-static
    DH involving the recipient's static key pair.  However, the binding
    between the recipient's alleged ephemeral public and the recipient's
    static public key has only been verified based on DHs involving both those
    public keys and the sender's static private key.  Thus, if the sender's
    static private key was previously compromised, the recipient's alleged
    ephemeral public key may have been forged by an active attacker.  In this
    case, the attacker could later compromise the intended recipient's static
    private key to decrypt the payload (this is a variant of a "KCI" attack
    enabling a "weak forward secrecy" attack). Note that a future version of
    Noise might include signatures, which could improve this security
    property, but brings other trade-offs.

 5. **Encryption to a known recipient, strong forward secrecy.**  This
    payload is encrypted based on an ephemeral-ephemeral DH as well as an
    ephemeral-static DH with the recipient's static key pair.  Assuming the
    ephemeral private keys are secure, and the recipient is not being actively
    impersonated by an attacker that has stolen its static private key, this
    payload cannot be decrypted.

For one-way handshakes, the below-listed security properties apply to the
handshake payload as well as transport payloads.

For interactive handshakes, security properties are listed for each handshake
payload.  Transport payloads are listed as arrows without a pattern.  Transport
payloads are only listed if they have different security properties than the
previous handshake payload sent from the same party.  If two transport payloads
are listed, the security properties for the second only apply if the first was
received.

+--------------------------------------------------------------+
|                              Source         Destination      |
+--------------------------------------------------------------+
|     N                           0                2           | 
+--------------------------------------------------------------+
|     K                           1                2           |
+--------------------------------------------------------------+
|     X                           1                2           |
+--------------------------------------------------------------+
|     NN                                                       |             
|       -> e                      0                0           |               
|       <- e, ee                  0                1           |               
|       ->                        0                1           |               
+--------------------------------------------------------------+
|     NK                                                       |                                 
|       <- s                                                   |
|       ...                                                    |                                 
|       -> e, es                  0                2           |               
|       <- e, ee                  2                1           |               
|       ->                        0                5           |               
+--------------------------------------------------------------+
|     NX                                                       |             
|       -> e                      0                0           |               
|       <- e, ee, s, es           2                1           |               
|       ->                        0                5           |               
+--------------------------------------------------------------+
|     XN                                                       |                                 
|       -> e                      0                0           |               
|       <- e, ee                  0                1           |               
|       -> s, se                  2                1           |               
|       <-                        0                5           |               
|                                                              |                                 
+--------------------------------------------------------------+
|     XK                                                       |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e, es                  0                2           |               
|       <- e, ee                  2                1           |               
|       -> s, se                  2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     XX                                                       |                                 
|       -> e                      0                0           |               
|       <- e, ee, s, es           2                1           |               
|       -> s, se                  2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     KN                                                       |                                 
|       -> s                                                   |                                 
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, se              0                3           |               
|       ->                        2                1           |               
|       <-                        0                5           |               
+--------------------------------------------------------------+
|     KK                                                       |                                 
|       -> s                                                   |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e, es, ss              1                2           |               
|       <- e, ee, se              2                4           |               
|       ->                        2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     KX                                                       |                           
|       -> s                                                   |                           
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, se, s, es       2                3           |               
|       ->                        2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     IN                                                       |    
|       -> e, s                   0                0           |         
|       <- e, ee, se              0                3           |         
|       ->                        2                1           |         
|       <-                        0                5           |         
+--------------------------------------------------------------+
|     IK                                                       |                        
|       <- s                                                   |                        
|       ...                                                    |                        
|       -> e, es, s, ss           1                2           |         
|       <- e, ee, se              2                4           |         
|       ->                        2                5           |         
|       <-                        2                5           |         
+--------------------------------------------------------------+
|     IX                                                       |                        
|       -> e, s                   0                0           |         
|       <- e, ee, se, s, es       2                3           |         
|       ->                        2                5           |         
|       <-                        2                5           |         
+--------------------------------------------------------------+


## 7.7. Identity hiding

The following table lists the identity-hiding properties for all the one-way
handshake patterns in [Section 7.4](#one-way-handshake-patterns) and the fundamental handshake patterns in [Section 7.5](#interactive-handshake-patterns).  In addition, we list a few deferred handshake patterns which have different identity-hiding properties than the corresponding fundamental pattern.

Each pattern is assigned properties describing the confidentiality supplied to
the initiator's static public key, and to the responder's static public key.
The underlying assumptions are that ephemeral private keys are secure, and that
parties abort the handshake if they receive a static public key from the other
party which they don't trust.

This section only considers identity leakage through static public key fields
in handshakes.  Of course, the identities of Noise participants might be
exposed through other means, including payload fields, traffic analysis, or
metadata such as IP addresses.

The properties for the relevant public key are:

  0. Transmitted in clear.

  1. Encrypted with forward secrecy, but can be probed by an
     anonymous initiator.

  2. Encrypted with forward secrecy, but sent to an anonymous responder. 

  3. Not transmitted, but a passive attacker can check candidates for the
     responder's private key and determine whether the candidate is correct.
     An attacker could also replay a previously-recorded message to a new
     responder and determine whether the two responders are the "same" (i.e. are
     using the same static key pair) by whether the recipient accepts the message.

  4. Encrypted to responder's static public key, without forward secrecy.
     If an attacker learns the responder's private key they can decrypt the
     initiator's public key. 

  5. Not transmitted, but a passive attacker can check candidates for the pair
     of (responder's private key, initiator's public key) and learn whether the
     candidate pair is correct.

  6. Encrypted but with weak forward secrecy.  An active attacker who
     pretends to be the initiator without the initiator's static private key,
     then later learns the initiator private key, can then decrypt the
     responder's public key.

  7. Not transmitted, but an active attacker who pretends to be the
     initator without the initiator's static private key, then later learns a
     candidate for the initiator private key, can then check whether the
     candidate is correct.

  8. Encrypted with forward secrecy to an authenticated party.

  9. An active attacker who pretends to be the initiator and records a single
     protocol run can then check candidates for the responder's public key.

<!-- end of list - necesary to trick Markdown into seeing the following -->

+------------------------------------------+
|                Initiator      Responder  |           
+------------------------------------------+
|     N              -              3      |
+------------------------------------------+
|     K              5              5      |
+------------------------------------------+
|     X              4              3      |
+------------------------------------------+
|     NN             -              -      |
+------------------------------------------+
|     NK             -              3      |
+------------------------------------------+
|     NK1            -              9      |
+------------------------------------------+
|     NX             -              1      |
+------------------------------------------+
|     XN             2              -      |
+------------------------------------------+
|     XK             8              3      |
+------------------------------------------+
|     XK1            8              9      |
+------------------------------------------+
|     XX             8              1      |
+------------------------------------------+
|     KN             7              -      |
+------------------------------------------+
|     KK             5              5      |
+------------------------------------------+
|     KX             7              6      |
+------------------------------------------+
|     IN             0              -      |
+------------------------------------------+
|     IK             4              3      |
+------------------------------------------+
|     IK1            4              9      |
+------------------------------------------+
|     IX             0              6      |
+------------------------------------------+

\newpage

# 8. Protocol names and modifiers

To produce a **Noise protocol name** for `Initialize()` you concatenate the
ASCII string `"Noise_"` with four underscore-separated name sections which
sequentially name the handshake pattern, the DH functions, the cipher
functions, and then the hash functions.  The resulting name must be 255 bytes
or less.  Examples:

 * `Noise_XX_25519_AESGCM_SHA256`
 * `Noise_N_25519_ChaChaPoly_BLAKE2s`
 * `Noise_IK_448_ChaChaPoly_BLAKE2b`

Each name section must consist only of alphanumeric characters (i.e. characters
in one of the ranges `"A"`...`"Z"`, `"a"`...`"z"`, and `"0"`...`"9"`), and the two special
characters `"+"` and `"/"`.

Additional rules apply to each name section, as specified below.

## 8.1. Handshake pattern name section

A handshake pattern name section contains a handshake pattern name plus a
sequence of zero or more **pattern modifiers**.

The handshake pattern name must be an uppercase ASCII string containing only
alphabetic characters or numerals (e.g. `"XX1"` or `"IK"`).

Pattern modifiers specify arbitrary extensions or modifications to the behavior
specified by the handshake pattern.  For example, a modifier could be applied
to a handshake pattern which transforms it into a different pattern according
to some rule.  The `"psk0"` and `"fallback"` modifiers are examples of this, 
and will be defined later in this document.

A pattern modifier is named with a lowercase alphanumeric ASCII string which
must begin with an alphabetic character (not a numeral).  The pattern modifier
is appended to the base pattern as described below:

The first modifier added onto a base pattern is simply appended.  Thus
the `"fallback"` modifier, when added to the `"XX"` pattern, produces `"XXfallback"`.
Additional modifiers are separated with a plus sign.  Thus, adding the `"psk0"`
modifier would result in the name section `"XXfallback+psk0"`, or a
full protocol name such as `"Noise_XXfallback+psk0_25519_AESGCM_SHA256"`.

In some cases the sequential ordering of modifiers will specify different
protocols.  However, if the order of some modifiers does not matter, then they are
required to be sorted alphabetically (this is an arbitrary convention to ensure
interoperability).

## 8.2. Cryptographic algorithm name sections

The rules for the DH, cipher, and hash name sections are identical.  Each name
section must contain one or more algorithm names separated by plus signs.  

Each algorithm name must consist solely of alphanumeric characters and the
forward-slash character (`"/"`).  Algorithm names are recommended to be short,
and to use the `"/"` character only when necessary to avoid ambiguity (e.g.
`"SHA3/256"` is preferable to `"SHA3256"`).

In most cases there will be a single algorithm name in each name section (i.e.
no plus signs).  Multiple algorithm names are only used when called for by the
pattern or a modifier.  

None of the patterns or modifiers in this document require multiple algorithm
names in any name section.  However, this functionality might be useful in
future extensions.  For example, multiple algorithm names might be used in the
DH section to specify "hybrid" post-quantum forward secrecy; or multiple hash
algorithms might be specified for different purposes.

# 9. Pre-shared symmetric keys

Noise provides a **pre-shared symmetric key** or **PSK** mode to support
protocols where both parties have a 32-byte shared secret key.

## 9.1. Cryptographic functions

PSK mode uses the `SymmetricState.MixKeyAndHash()` function to mix the PSK into both the encryption keys and the `h` value.

Note that `MixKeyAndHash()` uses `HKDF(..., 3)`.  The third output from `HKDF()` is used as the `k` value so that calculation of `k` may be skipped if `k` is not used.

## 9.2. Handshake tokens

In a PSK handshake, a `"psk"` token is allowed to appear one or more times in a
handshake pattern.  This token can only appear in message patterns (not
pre-message patterns).  This token is processed by calling
`MixKeyAndHash(psk)`, where `psk` is a 32-byte secret value provided by the
application.

In non-PSK handshakes, the `"e"` token in a pre-message pattern or message pattern always
results in a call to `MixHash(e.public_key)`.  In a PSK handshake, all of these calls
are followed by `MixKey(e.public_key)`.  In conjunction with the validity rule in the
next section, this ensures that PSK-based encryption uses encryption keys that are randomized using
ephemeral public keys as nonces.

## 9.3. Validity rule

To prevent catastrophic key reuse, handshake patterns using the `"psk"` token must follow an additional validity rule:

 * A party may not send any encrypted data after it processes a `"psk"` token unless it has previously 
 sent an ephemeral public key (an `"e"` token), either before or after the `"psk"` token.

This rule guarantees that a `k` derived from a PSK will never be used for
encryption unless it has also been randomized by `MixKey(e.public_key)`
using a self-chosen ephemeral public key.

## 9.4. Pattern modifiers

To indicate PSK mode and the placement of the `"psk"` token, pattern modifiers
are used (see [Section 8](#protocol-names-and-modifiers)).  The modifier `psk0` places a `"psk"`
token at the beginning of the first handshake message.  The modifiers
`psk1`, `psk2`, etc., place a `"psk"` token at the end of the
first, second, etc., handshake message.  

Any pattern using one of these modifiers must process tokens according to the rules in [Section 9.2](#handshake-tokens]), and must follow the validity rule in [Section 9.3](#validity-rule). 

The table below lists some unmodified one-way patterns on the left, and the recommended
PSK pattern on the right:


+--------------------------------+--------------------------------------+ 
|     N:                         |        Npsk0:                        | 
|       <- s                     |          <- s                        | 
|       ...                      |          ...                         | 
|       -> e, es                 |          -> psk, e, es               | 
|                                |                                      | 
+--------------------------------+--------------------------------------+ 
|     K:                         |        Kpsk0:                        | 
|       -> s                     |          -> s                        | 
|       <- s                     |          <- s                        | 
|       ...                      |          ...                         | 
|       -> e, es, ss             |          -> psk, e, es, ss           | 
|                                |                                      | 
+--------------------------------+--------------------------------------+ 
|     X:                         |        Xpsk1:                        | 
|       <- s                     |          <- s                        | 
|       ...                      |          ...                         | 
|       -> e, es, s, ss          |          -> e, es, s, ss, psk        | 
|                                |                                      | 
+--------------------------------+--------------------------------------+ 

Note that the `psk1` modifier is recommended for `X`.  This is because
`X` transmits the initiator's static public key.  Because PSKs are
typically pairwise, the responder likely cannot determine the PSK until it has
decrypted the initiator's static public key.  Thus, `psk1` is likely to be more
useful here than `psk0`.

Following similar logic, we can define the most likely interactive PSK patterns:

+--------------------------------+--------------------------------------+       
|     NN:                        |     NNpsk0:                          |
|       -> e                     |       -> psk, e                      |
|       <- e, ee                 |       <- e, ee                       |
+--------------------------------+--------------------------------------+
|     NN:                        |     NNpsk2:                          |
|       -> e                     |       -> e                           |
|       <- e, ee                 |       <- e, ee, psk                  |
+--------------------------------+--------------------------------------+
|     NK:                        |     NKpsk0:                          |
|       <- s                     |       <- s                           |
|       ...                      |       ...                            |
|       -> e, es                 |       -> psk, e, es                  |
|       <- e, ee                 |       <- e, ee                       |
+--------------------------------+--------------------------------------+
|     NK:                        |     NKpsk2:                          |
|       <- s                     |       <- s                           |
|       ...                      |       ...                            |
|       -> e, es                 |       -> e, es                       |
|       <- e, ee                 |       <- e, ee, psk                  |
+--------------------------------+--------------------------------------+
|     NX:                        |      NXpsk2:                         |
|       -> e                     |        -> e                          |
|       <- e, ee, s, es          |        <- e, ee, s, es, psk          |
+--------------------------------+--------------------------------------+
|     XN:                        |      XNpsk3:                         |
|       -> e                     |        -> e                          |
|       <- e, ee                 |        <- e, ee                      |
|       -> s, se                 |        -> s, se, psk                 |
+--------------------------------+--------------------------------------+
|     XK:                        |      XKpsk3:                         |
|       <- s                     |        <- s                          |
|       ...                      |        ...                           |
|       -> e, es                 |        -> e, es                      |
|       <- e, ee                 |        <- e, ee                      |
|       -> s, se                 |        -> s, se, psk                 |
+--------------------------------+--------------------------------------+
|     XX:                        |      XXpsk3:                         |
|       -> e                     |        -> e                          |
|       <- e, ee, s, es          |        <- e, ee, s, es               |
|       -> s, se                 |        -> s, se, psk                 |
+--------------------------------+--------------------------------------+   
|     KN:                        |       KNpsk0:                        |
|       -> s                     |         -> s                         |
|       ...                      |         ...                          |
|       -> e                     |         -> psk, e                    |
|       <- e, ee, se             |         <- e, ee, se                 |
+--------------------------------+--------------------------------------+   
|     KN:                        |       KNpsk2:                        |
|       -> s                     |         -> s                         |
|       ...                      |         ...                          |
|       -> e                     |         -> e                         |
|       <- e, ee, se             |         <- e, ee, se, psk            |
+--------------------------------+--------------------------------------+
|     KK:                        |       KKpsk0:                        |
|       -> s                     |         -> s                         |
|       <- s                     |         <- s                         |
|       ...                      |         ...                          |
|       -> e, es, ss             |         -> psk, e, es, ss            |
|       <- e, ee, se             |         <- e, ee, se                 |
+--------------------------------+--------------------------------------+
|     KK:                        |       KKpsk2:                        |
|       -> s                     |         -> s                         |
|       <- s                     |         <- s                         |
|       ...                      |         ...                          |
|       -> e, es, ss             |         -> e, es, ss                 |
|       <- e, ee, se             |         <- e, ee, se, psk            |
+--------------------------------+--------------------------------------+
|     KX:                        |        KXpsk2:                       |
|       -> s                     |          -> s                        |
|       ...                      |          ...                         |
|       -> e                     |          -> e                        |
|       <- e, ee, se, s, es      |          <- e, ee, se, s, es, psk    |
+--------------------------------+--------------------------------------+
|     IN:                        |        INpsk1:                       |
|       -> e, s                  |          -> e, s, psk                |
|       <- e, ee, se             |          <- e, ee, se                |
|                                |                                      |
+--------------------------------+--------------------------------------+
|     IN:                        |        INpsk2:                       |
|       -> e, s                  |          -> e, s                     |
|       <- e, ee, se             |          <- e, ee, se, psk           |
|                                |                                      |
+--------------------------------+--------------------------------------+
|     IK:                        |        IKpsk1:                       |
|       <- s                     |          <- s                        |
|       ...                      |          ...                         |
|       -> e, es, s, ss          |          -> e, es, s, ss, psk        |
|       <- e, ee, se             |          <- e, ee, se                |
|                                |                                      |
+--------------------------------+--------------------------------------+
|     IK:                        |        IKpsk2:                       |
|       <- s                     |          <- s                        |
|       ...                      |          ...                         |
|       -> e, es, s, ss          |          -> e, es, s, ss             |
|       <- e, ee, se             |          <- e, ee, se, psk           |
|                                |                                      |
+--------------------------------+--------------------------------------+
|     IX:                        |        IXpsk2:                       |
|       -> e, s                  |          -> e, s                     |
|       <- e, ee, se, s, es      |          <- e, ee, se, s, es, psk    |
|                                |                                      |
+--------------------------------+--------------------------------------+

The above list does not exhaust all possible patterns that can be formed with
these modifiers.  In particular, any of these PSK modifiers can be safely
applied to any previously named pattern, resulting in patterns like
`IKpsk0`, `KKpsk1`, or even `XXpsk0+psk3`, which aren't
listed above.

This still doesn't exhaust all the ways that `"psk"` tokens could be used
outside of these modifiers (e.g. placement of `"psk"` tokens in the middle of a
message pattern).  Defining additional PSK modifiers is outside the scope of
this document.

# 10. Compound protocols

## 10.1. Rationale for compound protocols

So far we've assumed Alice and Bob wish to execute a single Noise protocol
chosen by the initiator (Alice).  However, there are a number of reasons why
Bob might wish to switch to a different Noise protocol after receiving 
Alice's first message.  For example:

 * Alice might have chosen a Noise protocol based on a cipher, DH function, or
   handshake pattern which Bob doesn't support.

 * Alice might have sent a "zero-RTT" encrypted initial message based on an out-of-date
 version of Bob's static public key or PSK.

Handling these scenarios requires a **compound protocol** where Bob switches
from the initial Noise protocol chosen by Alice to a new Noise protocol.  In such a
compound protocol the roles of initiator and responder would be reversed - Bob
would become the initiator of the new Noise protocol, and Alice the responder.

Compound protocols introduce significant complexity as Alice needs to advertise
the Noise protocol she is beginning with and the Noise protocol(s) she is
capable of switching to, and both parties have to negotiate a secure transition.

These details are largely out of scope for this document.  However, to give an
example of how compound protocols can be constructed, and to provide some
building blocks, the following sections define a **`fallback`** modifier and show
how it can be used to create a **Noise Pipe** compound protocol.  

Noise Pipes support the `XX` pattern, but also allow Alice to cache Bob's
static public key and attempt an `IK` handshake with 0-RTT encryption.

In case Bob can't decrypt Alice's initial `IK` message, he will switch to the
`XXfallback` pattern, which essentially allows the parties to complete an `XX`
handshake as if Alice had sent an `XX` initial message instead of an `IK` initial message. 

## 10.2. The `fallback` modifier

The `fallback` modifier converts an Alice-initiated pattern to a Bob-initiated
pattern by converting Alice's initial message to a pre-message that Bob must
receive through some other means (e.g. via an initial `IK` message from Alice).
After this conversion, the rest of the handshake pattern is interpreted as a
Bob-initiated handshake pattern.

For example, here is the `fallback` modifier applied to `XX` to produce `XXfallback`:

\newpage
&nbsp;

    XX:  
      -> e
      <- e, ee, s, es
      -> s, se

    XXfallback:                   
      -> e
      ...
      <- e, ee, s, es
      -> s, se

Note that `fallback` can only be applied to handshake patterns in Alice-initiated form where Alice's first message is capable of being interpreted as a pre-message (i.e. it must be either `"e"`, `"s"`, or `"e, s"`).

## 10.3. Zero-RTT and Noise protocols

A typical compound protocol for zero-RTT encryption involves three different Noise protocols:

 * A **full protocol** is used if Alice doesn't possess stored information about Bob that would enable zero-RTT encryption, or doesn't wish to use the zero-RTT handshake.

 * A **zero-RTT protocol** allows encryption of data in the initial message.

 * A **switch protocol** is triggered by Bob if he can't decrypt Alice's first zero-RTT handshake message.

There must be some way for Bob to distinguish the full versus zero-RTT cases
on receiving the first message.  If Alice makes a zero-RTT attempt, there must
be some way for her to distinguish the zero-RTT versus switch cases on receiving
the response.

For example, each handshake message could be preceded by some negotiation data,
such as a `type` byte (see [Section 13](#application-responsibilities)).  This
data is not part of the Noise message proper, but signals which Noise protocol
is being used.

## 10.4. Noise Pipes

This section defines the **Noise Pipe** compound protocol.  The following
handshake patterns satisfy the full, zero-RTT, and switch roles discussed in
the previous section, so can be used to provide a full handshake with a simple
zero-RTT option:

    XX:  
      -> e
      <- e, ee, s, es
      -> s, se

    IK:                   
      <- s                         
      ...
      -> e, es, s, ss          
      <- e, ee, se

    XXfallback:                   
      -> e
      ...
      <- e, ee, s, es
      -> s, se

The `XX` pattern is used for a **full handshake** if the parties haven't
communicated before, after which Alice can cache Bob's static
public key.  

The `IK` pattern is used for a **zero-RTT handshake**.  

The `XXfallback` pattern is used for a **switch handshake** if Bob fails to
decrypt an initial `IK` message (perhaps due to having changed his static key).

## 10.5. Handshake indistinguishability

Parties might wish to hide from an eavesdropper which type of handshake they are
performing.  For example, suppose parties are using Noise Pipes, and want to
hide whether they are performing a full handshake, zero-RTT handshake, or
fallback handshake.  

This is fairly easy:

 * The first three messages can have their payloads padded with random bytes to
   a constant size, regardless of which handshake is executed.

 * Bob will attempt to decrypt the first message as an `IK` message,
   and will switch to `XXfallback` if decryption fails.

 * An Alice who sends an `IK` initial message can use trial decryption
   to differentiate between a response using `IK` or `XXfallback`. 

 * An Alice attempting a full handshake will send an ephemeral public key, then
   random padding, and will use `XXfallback` to handle the response.  Note that
   `XX` isn't used, because the server can't distinguish an `XX` message from a
   failed `IK` attempt by using trial decryption.

This leaves the Noise ephemeral public keys in the clear.  Ephemeral public
keys are randomly chosen DH public values, but they will typically have enough
structure that an eavesdropper might suspect the parties are using Noise, even
if the eavesdropper can't distinguish the different handshakes.  To make the
ephemerals indistinguishable from random byte sequences, techniques like
Elligator [@elligator] could be used.

# 11. Advanced features

## 11.1. Dummy keys

Consider a protocol where an initiator will authenticate herself if the responder
requests it.  This could be viewed as the initiator choosing between patterns
like `NX` and `XX` based on some value inside the responder's first
handshake payload.  

Noise doesn't directly support this.  Instead, this could be simulated by
always executing `XX`.  The initiator can simulate the `NX` case by
sending a **dummy static public key** if authentication is not requested.  The
value of the dummy public key doesn't matter.

This technique is simple, since it allows use of a single handshake pattern.
It also doesn't reveal which option was chosen from message sizes or
computation time.  It could be extended to allow an `XX` pattern to
support any permutation of authentications (initiator only, responder only,
both, or none).  

Similarly, **dummy PSKs** (e.g. a PSK of all zeros) would allow a protocol to
optionally support PSKs.

## 11.2. Channel binding

Parties might wish to execute a Noise protocol, then perform authentication at
the application layer using signatures, passwords, or something else.

To support this, Noise libraries may call `GetHandshakeHash()` after the
handshake is complete and expose the returned value to the application as a
**handshake hash** which uniquely identifies the Noise session.

Parties can then sign the handshake hash, or hash it along with their password,
to get an authentication token which has a "channel binding" property: the
token can't be used by the receiving party with a different sesssion.

## 11.3. Rekey
Parties might wish to periodically update their cipherstate keys using a one-way function, so that a compromise of cipherstate keys will not decrypt older messages.  Periodic rekey might also be used to reduce the volume of data encrypted under a single cipher key (this is usually not important with good ciphers, though note the discussion on `AESGCM` data volumes in [Section 14](#security-considerations)).

To enable this, Noise supports a `Rekey()` function which may be called on a `CipherState`.

It is up to to the application if and when to perform rekey.  For example: 

 * Applications might perform **continuous rekey**, where they rekey the relevant cipherstate after every transport message sent or received.  This is simple and gives good protection to older ciphertexts, but might be difficult for implementations where changing keys is expensive.

 * Applications might rekey a cipherstate automatically after it has has been used to send or receive some number of messages.

 * Applications might choose to rekey based on arbitrary criteria, in which case they signal this to the other party by sending a message.

Applications must make these decisions on their own; there are no pattern modifiers which specify rekey behavior.

Note that rekey only updates the cipherstate's `k` value, it doesn't reset the cipherstate's `n` value, so applications performing rekey must still perform a new handshake if sending 2^64^ or more transport messages.

## 11.4. Out-of-order transport messages

In some use cases, Noise transport messages might be lost or arrive
out-of-order (e.g. when messages are sent over UDP).  To handle this, an
application protocol can send the `n` value used for encrypting each transport
message alongside that message.  On receiving such a message the recipient
would call the `SetNonce()` function on the receiving `CipherState` using the
received `n` value.  

Recipients doing this must track the received `n` values for which decryption
was successful and reject any message which repeats such a value, to prevent
replay attacks.

Note that lossy and out-of-order message delivery introduces many other concerns
(including out-of-order handshake messages and denial of service risks) which
are outside the scope of this document.

## 11.5. Half-duplex protocols
In some application protocols the parties strictly alternate sending messages.  In this case Noise can be used in a **half-duplex** mode [@blinker] where the first `CipherState` returned by `Split()` is used for encrypting messages in both directions, and the second `CipherState` returned by `Split()` is unused.  This allows some small optimizations, since `Split()` only has to calculate a single output `CipherState`, and both parties only need to store a single `CipherState` during the transport phase.

This feature must be used with extreme caution.  In particular, it would be a catastrophic security failure if the protocol is not strictly alternating and both parties encrypt different messages using the same `CipherState` and nonce value.


# 12. DH functions, cipher functions, and hash functions

## 12.1. The `25519` DH functions

 * **`GENERATE_KEYPAIR()`**: Returns a new Curve25519 key pair.
 
 * **`DH(keypair, public_key)`**: Executes the Curve25519 DH function (aka
   "X25519" in [@rfc7748]).  Invalid public key values will produce an output
   of all zeros.  
   
     Alternatively, implementations are allowed to detect inputs that 
     produce an all-zeros output and signal an error instead.  This behavior is
     discouraged because it adds complexity and implementation variance, and
     does not improve security.  This behavior is allowed because it might
     match the behavior of some software.

 * **`DHLEN`** = 32

## 12.2. The `448` DH functions

 * **`GENERATE_KEYPAIR()`**: Returns a new Curve448 key pair.
 
 * **`DH(keypair, public_key)`**: Executes the Curve448 DH function (aka "X448"
   in [@rfc7748]).  Invalid public key values will produce an output of all
   zeros.  

     Alternatively, implementations are allowed to detect inputs that 
     produce an all-zeros output and signal an error instead.  This behavior is
     discouraged because it adds complexity and implementation variance, and
     does not improve security.  This behavior is allowed because it might
     match the behavior of some software.

 * **`DHLEN`** = 56

## 12.3. The `ChaChaPoly` cipher functions

 * **`ENCRYPT(k, n, ad, plaintext)` / `DECRYPT(k, n, ad, ciphertext)`**:
   `AEAD_CHACHA20_POLY1305` from [@rfc7539].  The 96-bit nonce is formed by
   encoding 32 bits of zeros followed by little-endian encoding of `n`.
   (Earlier implementations of ChaCha20 used a 64-bit nonce; with these
   implementations it's compatible to encode `n` directly into the ChaCha20
   nonce without the 32-bit zero prefix).

## 12.4. The `AESGCM` cipher functions

 * **`ENCRYPT(k, n, ad, plaintext)` / `DECRYPT(k, n, ad, ciphertext)`**: AES256
   with GCM from [@nistgcm] with a 128-bit tag appended to the
   ciphertext.  The 96-bit nonce is formed by encoding 32 bits of zeros
   followed by big-endian encoding of `n`.

## 12.5. The `SHA256` hash function

 * **`HASH(input)`**: `SHA-256` from [@nistsha2].
 * **`HASHLEN`** = 32
 * **`BLOCKLEN`** = 64

## 12.6. The `SHA512` hash function

 * **`HASH(input)`**: `SHA-512`  from [@nistsha2].
 * **`HASHLEN`** = 64
 * **`BLOCKLEN`** = 128

## 12.7. The `BLAKE2s` hash function

 * **`HASH(input)`**: `BLAKE2s` from [@rfc7693] with digest length 32.
 * **`HASHLEN`** = 32
 * **`BLOCKLEN`** = 64

## 12.8. The `BLAKE2b` hash function

 * **`HASH(input)`**: `BLAKE2b` from [@rfc7693] with digest length 64.
 * **`HASHLEN`** = 64
 * **`BLOCKLEN`** = 128

\newpage

# 13. Application responsibilities

An application built on Noise must consider several issues:

 * **Choosing crypto functions**:  The `25519` DH functions are recommended for
   typical uses, though the `448` DH functions might offer extra security
   in case a cryptanalytic attack is developed against elliptic curve
   cryptography.  The `448` DH functions should be used with a 512-bit hash
   like `SHA512` or `BLAKE2b`.  The `25519` DH functions may be used with a
   256-bit hash like `SHA256` or `BLAKE2s`, though a 512-bit hash might offer
   extra security in case a cryptanalytic attack is developed
   against the smaller hash functions.  `AESGCM` is hard to implement with
   high speed and constant time in software.

 * **Extensibility**:  Applications are recommended to use an extensible data
   format for the payloads of all messages (e.g. JSON, Protocol Buffers).  This
   ensures that fields can be added in the future which are ignored by older
   implementations.

 * **Padding**:  Applications are recommended to use a data format for the
   payloads of all encrypted messages that allows padding.  This allows
   implementations to avoid leaking information about message sizes.  Using an
   extensible data format, per the previous bullet, may be sufficient.

 * **Session termination**: Applications must consider that a sequence of Noise
   transport messages could be truncated by an attacker.  Applications should
   include explicit length fields or termination signals inside of transport
   payloads to signal the end of an interactive session, or the end of a
   one-way stream of transport messages. 

 * **Length fields**:  Applications must handle any framing or additional
   length fields for Noise messages, considering that a Noise message may be up
   to 65535 bytes in length.  If an explicit length field is needed,
   applications are recommended to add a 16-bit big-endian length field prior
   to each message.

 * **Negotiation data**:  Applications might wish to support the transmission
   of some negotiation data prior to the handshake, and/or prior to each
   handshake message.  Negotiation data could contain things like version
   information and identifiers for Noise protocols.  For example, a simple
   approach would be to send a single-byte type field prior to each Noise
   handshake message.  More flexible approaches might send extensible
   structures such as protobufs.  Negotiation data introduces significant
   complexity and security risks such as rollback attacks (see next section).

\newpage

# 14. Security considerations

This section collects various security considerations:

 * **Authentication**:  A Noise protocol with static public keys verifies that
   the corresponding private keys are possessed by the participant(s), but it's
   up to the application to determine whether the remote party's static public
   key is acceptable.  Methods for doing so include certificates which sign the
   public key (and which may be passed in handshake payloads), preconfigured
   lists of public keys, or "pinning" / "key-continuity" approaches where
   parties remember public keys they encounter and check whether the same party
   presents the same public key in the future.

 * **Session termination**:  Preventing attackers from truncating a stream of
   transport messages is an application responsibility.  See previous section.

 * **Rollback**:  If parties decide on a Noise protocol based on some previous
   negotiation that is not included as prologue, then a rollback attack might
   be possible.  This is a particular risk with compound protocols,
   and requires careful attention if a Noise handshake is preceded by
   communication between the parties.

 * **Misusing public keys as secrets**: It might be tempting to use a pattern
   with a pre-message public key and assume that a successful handshake implies
   the other party's knowledge of the public key.  Unfortunately, this is not
   the case, since setting public keys to invalid values might cause
   predictable DH output.  For example, a `Noise_NK_25519` initiator might send
   an invalid ephemeral public key to cause a known DH output of all zeros,
   despite not knowing the responder's static public key. If the parties want
   to authenticate with a shared secret, it should be used as a PSK.

 * **Channel binding**:  Depending on the DH functions, it might be possible
   for a malicious party to engage in multiple sessions that derive the same
   shared secret key by setting public keys to invalid values that cause
   predictable DH output (as in the previous bullet).  It might also be
   possible to set public keys to equivalent values that cause the same DH
   output for different inputs.  This is why a higher-level protocol should use
   the handshake hash (`h`) for a unique channel binding, instead of `ck`, as
   explained in [Section 11.2](#channel-binding).

 * **Incrementing nonces**:  Reusing a nonce value for `n` with the same key
   `k` for encryption would be catastrophic.  Implementations must carefully
   follow the rules for nonces.  Nonces are not allowed to wrap back to zero
   due to integer overflow, and the maximum nonce value is reserved.  This
   means parties are not allowed to send more than 2^64^-1 transport messages.

 * **Fresh ephemerals**:  Every party in a Noise protocol must send a fresh
   ephemeral public key prior to sending any encrypted data.  Ephemeral keys
   must never be reused.  Violating these rules is likely to cause catastrophic
   key reuse. This is one rationale behind the patterns in [Section   7](#handshake-patterns), 
   and the validity rules in [Section 7.3](#handshake-pattern-validity).  It's also the 
   reason why one-way handshakes only allow transport messages from the sender, 
   not the recipient.

 * **Protocol names**:  The protocol name used with `Initialize()` must
   uniquely identify the combination of handshake pattern and crypto functions
   for every key it's used with (whether ephemeral key pair, static key pair,
   or PSK).  If the same secret key was reused with the same protocol name but
   a different set of cryptographic operations then bad interactions could
   occur.

 * **Pre-shared symmetric keys**:  Pre-shared symmetric keys must be secret
   values with 256 bits of entropy.

 * **Data volumes**:  The `AESGCM` cipher functions suffer a gradual reduction
   in security as the volume of data encrypted under a single key increases.
   Due to this, parties should not send more than 2^56^ bytes (roughly 72
   petabytes) encrypted by a single key.  If sending such large volumes of data
   is a possibility then different cipher functions should be chosen.

 * **Hash collisions**:  If an attacker can find hash collisions on prologue
   data or the handshake hash, they may be able to perform "transcript
   collision" attacks that trick the parties into having different views of
   handshake data.  It is important to use Noise with
   collision-resistant hash functions, and replace the hash function at any
   sign of weakness.

 * **Implementation fingerprinting**:  If this protocol is used in settings
   with anonymous parties, care should be taken that implementations behave
   identically in all cases.  This may require mandating exact behavior for
   handling of invalid DH public keys.


# 15. Rationales

This section collects various design rationales.

## 15.1. Ciphers and encryption

Cipher keys and PSKs are 256 bits because:

  * 256 bits is a conservative length for cipher keys when considering
    cryptanalytic safety margins, time/memory tradeoffs, multi-key attacks,
    rekeying, and quantum attacks.

  * Pre-shared key length is fixed to simplify testing and implementation, and
    to deter users from mistakenly using low-entropy passwords as pre-shared keys.

Nonces are 64 bits because:

  * Some ciphers only have 64 bit nonces (e.g. Salsa20).

  * 64 bit nonces were used in the initial specification and implementations 
    of ChaCha20, so Noise nonces can be used with these implementations.

  * 64 bits makes it easy for the entire nonce to be treated as an integer 
    and incremented.

  * 96 bits nonces (e.g. in RFC 7539) are a confusing size where it's unclear if
    random nonces are acceptable.

The authentication data in a ciphertext (i.e. the authentication tag or synthetic IV) is 128 bits because:

  * Some algorithms (e.g. GCM) lose more security than an ideal MAC when 
    truncated.

  * Noise may be used in a wide variety of contexts, including where attackers
    can receive rapid feedback on whether guesses for authentication data are correct.

  * A single fixed length is simpler than supporting variable-length tags.

Ciphertexts are required to be indistinguishable from random because:

  * This makes Noise protocols easier to use with random padding (for length-hiding), or
  for censorship-resistant "unfingerprintable" protocols, or with steganography.  However note
  that ephemeral keys are likely to be distinguishable from random unless a technique such
  as Elligator [@elligator] is used.

Rekey defaults to using encryption with the nonce 2^64^-1 because:

  * With `AESGCM` and `ChaChaPoly` rekey can be computed efficiently (the
    "encryption" just needs to apply the cipher, and can skip calculation of
    the authentication tag).

Rekey doesn't reset `n` to zero because:

  * Leaving `n` unchanged is simple.

  * If the cipher has a weakness such that repeated rekeying gives rise to a cycle of keys, then letting `n` advance will avoid catastrophic reuse of the same `k` and `n` values.

  * Letting `n` advance puts a bound on the total number of encryptions that can be performed with a set of derived keys.

The `AESGCM` data volume limit is 2^56^ bytes because:

  * This is 2^52^ AES blocks (each block is 16 bytes).  The limit is based on
   the risk of birthday collisions being used to rule out plaintext guesses.
   The probability an attacker could rule out a random guess on a 2^56^ byte
   plaintext is less than 1 in 1 million (roughly (2^52^ * 2^52^) / 2^128^).

Cipher nonces are big-endian for `AESGCM`, and little-endian for `ChaCha20`, because:

  * ChaCha20 uses a little-endian block counter internally.

  * AES-GCM uses a big-endian block counter internally.

  * It makes sense to use consistent endianness in the cipher code.


## 15.2. Hash functions and hashing

The recommended hash function families are SHA2 and BLAKE2 because:

  * SHA2 is widely available and is often used alongside AES.

  * BLAKE2 is fast and similar to ChaCha20.

Hash output lengths of both 256 bits and 512 bits are supported because:

  * 256-bit hashes provide sufficient collision resistance at the 128-bit
    security level.

  * The 256-bit hashes (SHA-256 and BLAKE2s) require less RAM, and less computation when processing 
    smaller inputs (due to smaller block size), than SHA-512 and BLAKE2b.

  * SHA-256 and BLAKE2s are faster on 32-bit processors than the larger hashes, which use 64-bit operations internally.

The `MixKey()` design uses HKDF because:

  * HKDF is well-known and HKDF "chains" are used in similar ways in other protocols (e.g.
    Signal, IPsec, TLS 1.3).

  * HKDF has a published analysis [@hkdfpaper].

  * HKDF applies multiple layers of hashing between each `MixKey()` input.  This
    "extra" hashing might mitigate the impact of hash function weakness.

HMAC is used with all hash functions instead of allowing hashes to use a more
specialized function (e.g. keyed BLAKE2), because:

  * HKDF requires the use of HMAC, and some of the HKDF analysis in
    [@hkdfpaper] depends on the nested structure of HMAC.

  * HMAC is widely used with Merkle-Damgard hashes such as SHA2.  SHA3
    candidates such as Keccak and BLAKE were required to be suitable with HMAC.
    Thus, HMAC should be applicable to all widely-used hash functions. 

  * HMAC applies nested hashing to process each input.  This
    "extra" hashing might mitigate the impact of hash function weakness.

  * HMAC (and HKDF) are widely-used constructions.  If some weakness is found in a
    hash function, cryptanalysts will likely analyze that weakness in the
    context of HMAC and HKDF.

  * Applying HMAC consistently is simple, and avoids having custom designs with different
    cryptanalytic properties when using different hash functions.

  * HMAC is easy to build on top of a hash function interface.  If a more
    specialized function (e.g. keyed BLAKE2) can't be implemented using only
    the underlying hash, then it is not guaranteed to be available everywhere
    the hash function is available. 

`MixHash()` is used instead of sending all inputs directly through `MixKey()` because:

  * `MixHash()` is more efficient than `MixKey()`.

  * `MixHash()` produces a non-secret `h` value that might be useful to
     higher-level protocols, e.g. for channel-binding.

The `h` value hashes handshake ciphertext instead of plaintext because:

  * This ensures `h` is a non-secret value that can be used for channel-binding or
    other purposes without leaking secret information.

  * This provides stronger guarantees against ciphertext malleability. 


## 15.3. Other

Big-endian length fields are recommended because:

  * Length fields are likely to be handled by parsing code where 
    big-endian "network byte order" is traditional.

  * Some ciphers use big-endian internally (e.g. GCM, SHA2).

  * While it's true that Curve25519, Curve448, and ChaCha20/Poly1305 use 
    little-endian, these will likely be handled by specialized libraries, so 
    there's not a strong argument for aligning with them.

Session termination is left to the application because:

  * Providing a termination signal in Noise doesn't help the application much, 
    since the application still has to use the signal correctly.

  * For an application with its own termination signal, having a 
    second termination signal in Noise is likely to be confusing rather than helpful.

Explicit random nonces (like TLS "Random" fields) are not used because:

  * One-time ephemeral public keys make explicit nonces unnecessary.

  * Explicit nonces allow reuse of ephemeral public keys.  However reusing ephemerals (with periodic replacement) is more complicated, requires a secure time source, is less secure in case of ephemeral compromise, and only provides a small optimization, since key generation can be done for a fraction of the cost of a DH operation.

  * Explicit nonces increase message size.

  * Explicit nonces make it easier to "backdoor" crypto implementations, e.g. by modifying the RNG so that key recovery data is leaked through the nonce fields.


# 16. IPR

The Noise specification (this document) is hereby placed in the public domain.

# 17. Acknowledgements

Noise is inspired by:

  * The NaCl and CurveCP protocols from Dan Bernstein et al [@nacl; @curvecp].
  * The SIGMA and HOMQV protocols from Hugo Krawczyk [@sigma; @homqv].
  * The Ntor protocol from Ian Goldberg et al [@ntor].
  * The analysis of OTR by Mario Di Raimondo et al [@otr].
  * The analysis by Caroline Kudla and Kenny Paterson of "Protocol 4" by Simon Blake-Wilson et al [@kudla2005; @blakewilson1997].
  * Mike Hamburg's proposals for a sponge-based protocol framework, which led to STROBE [@moderncryptostrobe; @strobe].
  * The KDF chains used in the Double Ratchet Algorithm [@doubleratchet].

General feedback on the spec and design came from: Moxie Marlinspike, Jason
Donenfeld, Rhys Weatherley, Mike Hamburg, David Wong, Jake McGinty, Tiffany
Bennett, Jonathan Rudenberg, Stephen Touset, Tony Arcieri, Alex Wied, Alexey
Ermishkin, and Olaoluwa Osuntokun.

Helpful editorial feedback came from: Tom Ritter, Karthikeyan Bhargavan, David
Wong, Klaus Hartke, Dan Burkert, Jake McGinty, Yin Guanhao, Nazar Mokrynskyi,
Keziah Elis Biermann, Justin Cormack, Katriel Cohn-Gordon, and Nadim Kobeissi.

Helpful input and feedback on the key derivation design came from: Moxie
Marlinspike, Hugo Krawczyk, Samuel Neves, Christian Winnerlein, J.P. Aumasson,
and Jason Donenfeld.

The PSK approach was largely motivated and designed by Jason Donenfeld, based
on his experience with PSKs in WireGuard.

The deferred patterns resulted from discussions with Justin Cormack.

The security properties table for deferred patterns was derived by the 
Noise Explorer tool, from Nadim Kobeissi.

The rekey design benefited from discussions with Rhys Weatherley, Alexey
Ermishkin, and Olaoluwa Osuntokun.  

The BLAKE2 team (in particular J.P.  Aumasson, Samuel Neves, and Zooko)
provided helpful discussion on using BLAKE2 with Noise.

Jeremy Clark, Thomas Ristenpart, and Joe Bonneau gave feedback on earlier
versions.

\newpage

# 18. Appendices

## 18.1 Deferred patterns

The following table lists all 23 deferred handshake patterns in the right
column, with their corresponding fundamental handshake pattern in the left
column.  See [Section 7](#handshake-patterns) for an explanation of 
fundamental and deferred patterns.

+---------------------------+--------------------------------+
|     NK:                   |         NK1:                   |
|       <- s                |           <- s                 |
|       ...                 |           ...                  |
|       -> e, es            |           -> e                 |
|       <- e, ee            |           <- e, ee, es         |
|                           |                                |
+---------------------------+--------------------------------+
|     NX:                   |         NX1:                   |
|       -> e                |           -> e                 |
|       <- e, ee, s, es     |           <- e, ee, s          |
|                           |           -> es                |
|                           |                                |
+---------------------------+--------------------------------+
|     XN:                   |         X1N:                   |
|       -> e                |           -> e                 |
|       <- e, ee            |           <- e, ee             |
|       -> s, se            |           -> s                 |
|                           |           <- se                |
|                           |                                |
+---------------------------+--------------------------------+
|     XK:                   |         X1K:                   |
|       <- s                |           <- s                 |
|       ...                 |           ...                  |
|       -> e, es            |           -> e, es             |
|       <- e, ee            |           <- e, ee             |
|       -> s, se            |           -> s                 |
|                           |           <- se                |
|                           |                                |
|                           |         XK1:                   |
|                           |           <- s                 |
|                           |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, es         |
|                           |           -> s, se             |
|                           |                                |
|                           |         X1K1:                  |
|                           |           <- s                 |
|                           |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, es         |
|                           |           -> s                 |
|                           |           <- se                |
|                           |                                |
+---------------------------+--------------------------------+
|     XX:                   |         X1X:                   | 
|       -> e                |           -> e                 |
|       <- e, ee, s, es     |           <- e, ee, s, es      |
|       -> s, se            |           -> s                 |
|                           |           <- se                |
|                           |                                |
|                           |         XX1:                   |
|                           |           -> e                 |
|                           |           <- e, ee, s          |
|                           |           -> es, s, se         |
|                           |                                |
|                           |         X1X1:                  |
|                           |           -> e                 |
|                           |           <- e, ee, s          |
|                           |           -> es, s             |
|                           |           <- se                |
|                           |                                |
+---------------------------+--------------------------------+
|     KN:                   |         K1N:                   |
|       -> s                |           -> s                 |
|       ...                 |           ...                  |
|       -> e                |           -> e                 |
|       <- e, ee, se        |           <- e, ee             |
|                           |           -> se                |
|                           |                                |
+---------------------------+--------------------------------+
|     KK:                   |         K1K:                   | 
|       -> s                |           -> s                 |
|       <- s                |           <- s                 |
|       ...                 |           ...                  |
|       -> e, es, ss        |           -> e, es             |
|       <- e, ee, se        |           <- e, ee             |
|                           |           -> se                |
|                           |                                |
|                           |         KK1:                   |
|                           |           -> s                 |
|                           |           <- s                 |
|                           |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, se, es     |
|                           |                                |
|                           |         K1K1:                  |
|                           |           -> s                 |
|                           |           <- s                 |
|                           |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, es         |
|                           |           -> se                |
|                           |                                |
+---------------------------+--------------------------------+
|     KX:                   |         K1X:                   |
|       -> s                |           -> s                 |
|       ...                 |           ...                  |
|       -> e                |           -> e                 |
|       <- e, ee, se, s, es |           <- e, ee, s, es      |
|                           |           -> se                |
|                           |                                |
|                           |         KX1:                   |
|                           |           -> s                 |
|                           |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, se, s      |
|                           |           -> es                |
|                           |                                |
|                           |         K1X1:                  |
|                           |           -> s                 |
|                           |           ...                  |
|                           |           -> e                 |
|                           |           <- e, ee, s          |
|                           |           -> se, es            |
|                           |                                |
|                           |                                |
+---------------------------+--------------------------------+
|     IN:                   |         I1N:                   |
|       -> e, s             |           -> e, s              |
|       <- e, ee, se        |           <- e, ee             |
|                           |           -> se                |
|                           |                                |
+---------------------------+--------------------------------+
|     IK:                   |         I1K:                   |
|       <- s                |           <- s                 |
|       ...                 |           ...                  |
|       -> e, es, s, ss     |           -> e, es, s          |
|       <- e, ee, se        |           <- e, ee             |
|                           |           -> se                |
|                           |                                |
|                           |         IK1:                   |
|                           |           <- s                 |
|                           |           ...                  |
|                           |           -> e, s              |
|                           |           <- e, ee, se, es     |
|                           |                                |
|                           |         I1K1:                  |
|                           |           <- s                 |
|                           |           ...                  |
|                           |           -> e, s              |  
|                           |           <- e, ee, es         |
|                           |           -> se                | 
|                           |                                |
+---------------------------+--------------------------------+
|     IX:                   |         I1X:                   | 
|       -> e, s             |           -> e, s              |
|       <- e, ee, se, s, es |           <- e, ee, s, es      |
|                           |           -> se                |
|                           |                                |
|                           |         IX1:                   |
|                           |           -> e, s              |
|                           |           <- e, ee, se, s      |
|                           |           -> es                |
|                           |                                |
|                           |         I1X1:                  |
|                           |           -> e, s              |
|                           |           <- e, ee, s          |
|                           |           -> se, es            |
|                           |                                |
+---------------------------+--------------------------------+

\newpage

## 18.2. Security properties for deferred patterns

The following table lists the the security properties for the Noise handshake
and transport payloads for all the deferred patterns in the previous section.
The security properties are labelled using the notation from [Section 7.6](#payload-security-properties).

+--------------------------------------------------------------+
|                              Source         Destination      |
+--------------------------------------------------------------+
|     NK1                                                      |                                 
|       <- s                                                   |
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, es              2                1           |               
|       ->                        0                5           |               
+--------------------------------------------------------------+
|     NX1                                                      |             
|       -> e                      0                0           |               
|       <- e, ee, s               0                1           |               
|       -> es                     0                3           |               
|       ->                        2                1           |
|       <-                        0                5           |
+--------------------------------------------------------------+
|     X1N                                                      |                                 
|       -> e                      0                0           |               
|       <- e, ee                  0                1           |               
|       -> s                      0                1           |               
|       <- se                     0                3           |               
|       ->                        2                1           |
+--------------------------------------------------------------+
|     X1K                                                      |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e, es                  0                2           |               
|       <- e, ee                  2                1           |               
|       -> s                      0                5           |               
|       <- se                     2                3           |               
|       ->                        2                5           |
|       <-                        2                5           |
+--------------------------------------------------------------+
|     XK1                                                      |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, es              2                1           |               
|       -> s, se                  2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     X1K1                                                     |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, es              2                1           |               
|       -> s                      0                5           |               
|       <- se                     2                3           |               
|       ->                        2                5           |
|       <-                        2                5           |
+--------------------------------------------------------------+
|     X1X                                                      |                                 
|       -> e                      0                0           |               
|       <- e, ee, s, es           2                1           |               
|       -> s                      0                5           |               
|       <- se                     2                3           |               
|       ->                        2                5           |
|       <-                        2                5           |
+--------------------------------------------------------------+
|     XX1                                                      |                                 
|       -> e                      0                0           |               
|       <- e, ee, s               0                1           |               
|       -> es, s, se              2                3           |               
|       <-                        2                5           |
|       ->                        2                5           |
+--------------------------------------------------------------+
|     X1X1                                                     |                                 
|       -> e                      0                0           |               
|       <- e, ee, s               0                1           |               
|       -> es, s                  0                3           |               
|       <- se                     2                3           |               
|       ->                        2                5           |
|       <-                        2                5           |
+--------------------------------------------------------------+
|     K1N                                                      |                                 
|       -> s                                                   |                                 
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee                  0                1           |               
|       -> se                     2                1           |               
|       <-                        0                5           |               
+--------------------------------------------------------------+
|     K1K                                                      |                                 
|       -> s                                                   |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e, es                  0                2           |               
|       <- e, ee, se              2                1           |               
|       -> se                     2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     KK1                                                      |                                 
|       -> s                                                   |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, se, es          2                3           |               
|       ->                        2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     K1K1                                                     |                                 
|       -> s                                                   |                                 
|       <- s                                                   |                                 
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, es              2                1           |               
|       -> se                     2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     K1X                                                      |                           
|       -> s                                                   |                           
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, s, es           2                1           |               
|       -> se                     2                5           |               
|       <-                        2                5           |               
+--------------------------------------------------------------+
|     KX1                                                      |                           
|       -> s                                                   |                           
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, se, s           0                3           |               
|       -> es                     2                3           |               
|       <-                        2                5           |               
|       ->                        2                5           |
+--------------------------------------------------------------+
|     K1X1                                                     |                           
|       -> s                                                   |                           
|       ...                                                    |                                 
|       -> e                      0                0           |               
|       <- e, ee, s               0                1           |               
|       -> se, es                 2                3           |               
|       <-                        2                5           |               
|       ->                        2                5           |
+--------------------------------------------------------------+
|     I1N                                                      |    
|       -> e, s                   0                0           |         
|       <- e, ee                  0                1           |         
|       -> se                     2                1           |         
|       <-                        0                5           |         
+--------------------------------------------------------------+
|     I1K                                                      |                        
|       <- s                                                   |                        
|       ...                                                    |                        
|       -> e, es, s               0                2           |         
|       <- e, ee                  2                1           |         
|       -> se                     2                5           |         
|       <-                        2                5           |         
+--------------------------------------------------------------+
|     IK1                                                      |                        
|       <- s                                                   |                        
|       ...                                                    |                        
|       -> e, s                   0                0           |         
|       <- e, ee, se, es          2                3           |         
|       ->                        2                5           |         
|       <-                        2                5           |         
+--------------------------------------------------------------+
|     I1K1                                                     |                        
|       <- s                                                   |                        
|       ...                                                    |                        
|       -> e, s                   0                0           |         
|       <- e, ee, es              2                1           |         
|       -> se                     2                5           |         
|       <-                        2                5           |         
+--------------------------------------------------------------+
|     I1X                                                      |                        
|       -> e, s                   0                0           |         
|       <- e, ee, s, es           2                1           |         
|       -> se                     2                5           |         
|       <-                        2                5           |         
+--------------------------------------------------------------+
|     IX1                                                      |                        
|       -> e, s                   0                0           |         
|       <- e, ee, se, s           0                3           |         
|       -> es                     2                3           |         
|       <-                        2                5           |         
|       ->                        2                5           |         
+--------------------------------------------------------------+
|     I1X1                                                     |                        
|       -> e, s                   0                0           |         
|       <- e, ee, s               0                1           |         
|       -> se, es                 2                3           |         
|       <-                        2                5           |         
|       ->                        2                5           |         
+--------------------------------------------------------------+


# 18.3. Change log


**Revision 34:**

 * Added official/unstable marking; the unstable only refers to the new deferred patterns, the rest of this document is considered stable.

 * Clarified DH() definition so that the identity element is an invalid value which may be rejected.

 * Clarified ciphertext-indistinguishability requirement for AEAD schemes and added a rationale.

 * Clarified the order of hashing pre-message public keys.

 * Rewrote handshake patterns explanation for clarity.

 * Removed parenthesized list of keys from pattern notation, as it was redundant. 

 * Added deferred patterns.

 * Renamed "Authentication" and "Confidentiality" security properties to "Source" and "Destination" to avoid confusion.

 * Added a new identity-hiding property, and changed identity-hiding property 3 to discuss an identity equality-check attack. 

 * Replaced "fallback patterns" concept with Bob-initiated pattern notation.

 * Rewrote section on compound protocols and pipes for clarity, including
   clearer distinction between "switch protocol" and "fallback patterns".

 * De-emphasised "type byte" suggestion, and added a more general discussion of negotiation data.



# 19.  References