    Internet Research Task Force (IRTF)                               Y. Nir
    Request for Comments: 8439                                      Dell EMC
    Obsoletes: 7539                                               A. Langley
    Category: Informational                                     Google, Inc.
    ISSN: 2070-1721                                                June 2018

                    ChaCha20 and Poly1305 for IETF Protocols

    Abstract

       This document defines the ChaCha20 stream cipher as well as the use
       of the Poly1305 authenticator, both as stand-alone algorithms and as
       a "combined mode", or Authenticated Encryption with Associated Data
       (AEAD) algorithm.

       RFC 7539, the predecessor of this document, was meant to serve as a
       stable reference and an implementation guide.  It was a product of
       the Crypto Forum Research Group (CFRG).  This document merges the
       errata filed against RFC 7539 and adds a little text to the Security
       Considerations section.

    Status of This Memo

       This document is not an Internet Standards Track specification; it is
       published for informational purposes.

       This document is a product of the Internet Research Task Force
       (IRTF).  The IRTF publishes the results of Internet-related research
       and development activities.  These results might not be suitable for
       deployment.  This RFC represents the consensus of the Crypto Forum
       Research Group of the Internet Research Task Force (IRTF).  Documents
       approved for publication by the IRSG are not candidates for any level
       of Internet Standard; see Section 2 of RFC 7841.

       Information about the current status of this document, any errata,
       and how to provide feedback on it may be obtained at
       https://www.rfc-editor.org/info/rfc8439.

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    Copyright Notice

       Copyright (c) 2018 IETF Trust and the persons identified as the
       document authors.  All rights reserved.

       This document is subject to BCP 78 and the IETF Trust's Legal
       Provisions Relating to IETF Documents
       (https://trustee.ietf.org/license-info) in effect on the date of
       publication of this document.  Please review these documents
       carefully, as they describe your rights and restrictions with respect
       to this document.

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    Table of Contents

       1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
         1.1.  Conventions Used in This Document . . . . . . . . . . . .   5
       2.  The Algorithms  . . . . . . . . . . . . . . . . . . . . . . .   5
         2.1.  The ChaCha Quarter Round  . . . . . . . . . . . . . . . .   5
           2.1.1.  Test Vector for the ChaCha Quarter Round  . . . . . .   6
         2.2.  A Quarter Round on the ChaCha State . . . . . . . . . . .   6
           2.2.1.  Test Vector for the Quarter Round on the ChaCha State   7
         2.3.  The ChaCha20 Block Function . . . . . . . . . . . . . . .   7
           2.3.1.  The ChaCha20 Block Function in Pseudocode . . . . . .   9
           2.3.2.  Test Vector for the ChaCha20 Block Function . . . . .  10
         2.4.  The ChaCha20 Encryption Algorithm . . . . . . . . . . . .  11
           2.4.1.  The ChaCha20 Encryption Algorithm in Pseudocode . . .  12
           2.4.2.  Example and Test Vector for the ChaCha20 Cipher . . .  12
         2.5.  The Poly1305 Algorithm  . . . . . . . . . . . . . . . . .  14
           2.5.1.  The Poly1305 Algorithms in Pseudocode . . . . . . . .  16
           2.5.2.  Poly1305 Example and Test Vector  . . . . . . . . . .  17
         2.6.  Generating the Poly1305 Key Using ChaCha20  . . . . . . .  18
           2.6.1.  Poly1305 Key Generation in Pseudocode . . . . . . . .  19
           2.6.2.  Poly1305 Key Generation Test Vector . . . . . . . . .  19
         2.7.  A Pseudorandom Function for Crypto Suites Based on
               ChaCha/Poly1305 . . . . . . . . . . . . . . . . . . . . .  20
         2.8.  AEAD Construction . . . . . . . . . . . . . . . . . . . .  20
           2.8.1.  Pseudocode for the AEAD Construction  . . . . . . . .  23
           2.8.2.  Example and Test Vector for AEAD_CHACHA20_POLY1305  .  23
       3.  Implementation Advice . . . . . . . . . . . . . . . . . . . .  25
       4.  Security Considerations . . . . . . . . . . . . . . . . . . .  26
       5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  27
       6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  27
         6.1.  Normative References  . . . . . . . . . . . . . . . . . .  27
         6.2.  Informative References  . . . . . . . . . . . . . . . . .  28
       Appendix A.  Additional Test Vectors  . . . . . . . . . . . . . .  30
         A.1.  The ChaCha20 Block Functions  . . . . . . . . . . . . . .  30
         A.2.  ChaCha20 Encryption . . . . . . . . . . . . . . . . . . .  33
         A.3.  Poly1305 Message Authentication Code  . . . . . . . . . .  36
         A.4.  Poly1305 Key Generation Using ChaCha20  . . . . . . . . .  41
         A.5.  ChaCha20-Poly1305 AEAD Decryption . . . . . . . . . . . .  42
       Appendix B.  Performance Measurements of ChaCha20 . . . . . . . .  45
       Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  46
       Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  46

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    1.  Introduction

       The Advanced Encryption Standard (AES -- [FIPS-197]) has become the
       gold standard in encryption.  Its efficient design, widespread
       implementation, and hardware support allow for high performance in
       many areas.  On most modern platforms, AES is anywhere from four to
       ten times as fast as the previous most-used cipher, Triple Data
       Encryption Standard (3DES -- [SP800-67]), which makes it not only the
       best choice, but the only practical choice.

       There are several problems with this.  If future advances in
       cryptanalysis reveal a weakness in AES, users will be in an
       unenviable position.  With the only other widely supported cipher
       being the much slower 3DES, it is not feasible to reconfigure
       deployments to use 3DES.  [Standby-Cipher] describes this issue and
       the need for a standby cipher in greater detail.  Another problem is
       that while AES is very fast on dedicated hardware, its performance on
       platforms that lack such hardware is considerably lower.  Yet another
       problem is that many AES implementations are vulnerable to cache-
       collision timing attacks ([Cache-Collisions]).

       This document provides a definition and implementation guide for
       three algorithms:

       1.  The ChaCha20 cipher.  This is a high-speed cipher first described
           in [ChaCha].  It is considerably faster than AES in software-only
           implementations, making it around three times as fast on
           platforms that lack specialized AES hardware.  See Appendix B for
           some hard numbers.  ChaCha20 is also not sensitive to timing
           attacks (see the security considerations in Section 4).  This
           algorithm is described in Section 2.4

       2.  The Poly1305 authenticator.  This is a high-speed message
           authentication code.  Implementation is also straightforward and
           easy to get right.  The algorithm is described in Section 2.5.

       3.  The CHACHA20-POLY1305 Authenticated Encryption with Associated
           Data (AEAD) construction, described in Section 2.8.

       This document and its predecessor do not introduce these new
       algorithms for the first time.  They have been defined in scientific
       papers by D. J. Bernstein [ChaCha][Poly1305].  The purpose of this
       document is to serve as a stable reference for IETF documents making
       use of these algorithms.

       These algorithms have undergone rigorous analysis.  Several papers
       discuss the security of Salsa and ChaCha ([LatinDances],
       [LatinDances2], [Zhenqing2012]).

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       This document represents the consensus of the Crypto Forum Research
       Group (CFRG).  It replaces [RFC7539].

    1.1.  Conventions Used in This Document

       The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
       "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
       "OPTIONAL" in this document are to be interpreted as described in BCP
       14 [RFC2119] [RFC8174] when, and only when, they appear in all
       capitals, as shown here.

       The description of the ChaCha algorithm will at various time refer to
       the ChaCha state as a "vector" or as a "matrix".  This follows the
       use of these terms in [ChaCha].  The matrix notation is more visually
       convenient and gives a better notion as to why some rounds are called
       "column rounds" while others are called "diagonal rounds".  Here's a
       diagram of how the matrices relate to vectors (using the C language
       convention of zero being the index origin).

          0   1   2   3
          4   5   6   7
          8   9  10  11
         12  13  14  15

       The elements in this vector or matrix are 32-bit unsigned integers.

       The algorithm name is "ChaCha".  "ChaCha20" is a specific instance
       where 20 "rounds" (or 80 quarter rounds -- see Section 2.1) are used.
       Other variations are defined, with 8 or 12 rounds, but in this
       document we only describe the 20-round ChaCha, so the names "ChaCha"
       and "ChaCha20" will be used interchangeably.

    2.  The Algorithms

       The subsections below describe the algorithms used and the AEAD
       construction.

    2.1.  The ChaCha Quarter Round

       The basic operation of the ChaCha algorithm is the quarter round.  It
       operates on four 32-bit unsigned integers, denoted a, b, c, and d.
       The operation is as follows (in C-like notation):

          a += b; d ^= a; d <<<= 16;
          c += d; b ^= c; b <<<= 12;
          a += b; d ^= a; d <<<= 8;
          c += d; b ^= c; b <<<= 7;

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       Where "+" denotes integer addition modulo 2^32, "^" denotes a bitwise
       Exclusive OR (XOR), and "<<< n" denotes an n-bit left roll (towards
       the high bits).

       For example, let's see the add, XOR, and roll operations from the
       fourth line with sample numbers:

          a = 0x11111111
          b = 0x01020304
          c = 0x77777777
          d = 0x01234567
          c = c + d = 0x77777777 + 0x01234567 = 0x789abcde
          b = b ^ c = 0x01020304 ^ 0x789abcde = 0x7998bfda
          b = b <<< 7 = 0x7998bfda <<< 7 = 0xcc5fed3c

    2.1.1.  Test Vector for the ChaCha Quarter Round

       For a test vector, we will use the same numbers as in the example,
       adding something random for c.

          a = 0x11111111
          b = 0x01020304
          c = 0x9b8d6f43
          d = 0x01234567

       After running a Quarter Round on these four numbers, we get these:

          a = 0xea2a92f4
          b = 0xcb1cf8ce
          c = 0x4581472e
          d = 0x5881c4bb

    2.2.  A Quarter Round on the ChaCha State

       The ChaCha state does not have four integer numbers: it has 16.  So
       the quarter-round operation works on only four of them -- hence the
       name.  Each quarter round operates on four predetermined numbers in
       the ChaCha state.  We will denote by QUARTERROUND(x, y, z, w) a
       quarter-round operation on the numbers at indices x, y, z, and w of
       the ChaCha state when viewed as a vector.  For example, if we apply
       QUARTERROUND(1, 5, 9, 13) to a state, this means running the quarter-
       round operation on the elements marked with an asterisk, while
       leaving the others alone:

          0  *a   2   3
          4  *b   6   7
          8  *c  10  11
         12  *d  14  15

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       Note that this run of quarter round is part of what is called a
       "column round".

    2.2.1.  Test Vector for the Quarter Round on the ChaCha State

       For a test vector, we will use a ChaCha state that was generated
       randomly:

       Sample ChaCha State

           879531e0  c5ecf37d  516461b1  c9a62f8a
           44c20ef3  3390af7f  d9fc690b  2a5f714c
           53372767  b00a5631  974c541a  359e9963
           5c971061  3d631689  2098d9d6  91dbd320

       We will apply the QUARTERROUND(2, 7, 8, 13) operation to this state.
       For obvious reasons, this one is part of what is called a "diagonal
       round":

       After applying QUARTERROUND(2, 7, 8, 13)

           879531e0  c5ecf37d *bdb886dc  c9a62f8a
           44c20ef3  3390af7f  d9fc690b *cfacafd2
          *e46bea80  b00a5631  974c541a  359e9963
           5c971061 *ccc07c79  2098d9d6  91dbd320

       Note that only the numbers in positions 2, 7, 8, and 13 changed.

    2.3.  The ChaCha20 Block Function

       The ChaCha block function transforms a ChaCha state by running
       multiple quarter rounds.

       The inputs to ChaCha20 are:

       o  A 256-bit key, treated as a concatenation of eight 32-bit little-
          endian integers.

       o  A 96-bit nonce, treated as a concatenation of three 32-bit little-
          endian integers.

       o  A 32-bit block count parameter, treated as a 32-bit little-endian
          integer.

       The output is 64 random-looking bytes.

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       The ChaCha algorithm described here uses a 256-bit key.  The original
       algorithm also specified 128-bit keys and 8- and 12-round variants,
       but these are out of scope for this document.  In this section, we
       describe the ChaCha block function.

       Note also that the original ChaCha had a 64-bit nonce and 64-bit
       block count.  We have modified this here to be more consistent with
       recommendations in Section 3.2 of [RFC5116].  This limits the use of
       a single (key,nonce) combination to 2^32 blocks, or 256 GB, but that
       is enough for most uses.  In cases where a single key is used by
       multiple senders, it is important to make sure that they don't use
       the same nonces.  This can be assured by partitioning the nonce space
       so that the first 32 bits are unique per sender, while the other 64
       bits come from a counter.

       The ChaCha20 state is initialized as follows:

       o  The first four words (0-3) are constants: 0x61707865, 0x3320646e,
          0x79622d32, 0x6b206574.

       o  The next eight words (4-11) are taken from the 256-bit key by
          reading the bytes in little-endian order, in 4-byte chunks.

       o  Word 12 is a block counter.  Since each block is 64-byte, a 32-bit
          word is enough for 256 gigabytes of data.

       o  Words 13-15 are a nonce, which MUST not be repeated for the same
          key.  The 13th word is the first 32 bits of the input nonce taken
          as a little-endian integer, while the 15th word is the last 32
          bits.

           cccccccc  cccccccc  cccccccc  cccccccc
           kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
           kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
           bbbbbbbb  nnnnnnnn  nnnnnnnn  nnnnnnnn

       c=constant k=key b=blockcount n=nonce

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       ChaCha20 runs 20 rounds, alternating between "column rounds" and
       "diagonal rounds".  Each round consists of four quarter-rounds, and
       they are run as follows.  Quarter rounds 1-4 are part of a "column"
       round, while 5-8 are part of a "diagonal" round:

          QUARTERROUND(0, 4, 8, 12)
          QUARTERROUND(1, 5, 9, 13)
          QUARTERROUND(2, 6, 10, 14)
          QUARTERROUND(3, 7, 11, 15)
          QUARTERROUND(0, 5, 10, 15)
          QUARTERROUND(1, 6, 11, 12)
          QUARTERROUND(2, 7, 8, 13)
          QUARTERROUND(3, 4, 9, 14)

       At the end of 20 rounds (or 10 iterations of the above list), we add
       the original input words to the output words, and serialize the
       result by sequencing the words one-by-one in little-endian order.

       Note: "addition" in the above paragraph is done modulo 2^32.  In some
       machine languages, this is called carryless addition on a 32-bit
       word.

    2.3.1.  The ChaCha20 Block Function in Pseudocode

       Note: This section and a few others contain pseudocode for the
       algorithm explained in a previous section.  Every effort was made for
       the pseudocode to accurately reflect the algorithm as described in
       the preceding section.  If a conflict is still present, the textual
       explanation and the test vectors are normative.

          inner_block (state):
             Qround(state, 0, 4, 8, 12)
             Qround(state, 1, 5, 9, 13)
             Qround(state, 2, 6, 10, 14)
             Qround(state, 3, 7, 11, 15)
             Qround(state, 0, 5, 10, 15)
             Qround(state, 1, 6, 11, 12)
             Qround(state, 2, 7, 8, 13)
             Qround(state, 3, 4, 9, 14)
             end

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          chacha20_block(key, counter, nonce):
             state = constants | key | counter | nonce
             initial_state = state
             for i=1 upto 10
                inner_block(state)
                end
             state += initial_state
             return serialize(state)
             end

       Where the pipe character ("|") denotes concatenation.

    2.3.2.  Test Vector for the ChaCha20 Block Function

       For a test vector, we will use the following inputs to the ChaCha20
       block function:

       o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
          14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.  The key is a sequence of
          octets with no particular structure before we copy it into the
          ChaCha state.

       o  Nonce = (00:00:00:09:00:00:00:4a:00:00:00:00)

       o  Block Count = 1.

       After setting up the ChaCha state, it looks like this:

       ChaCha state with the key setup.

           61707865  3320646e  79622d32  6b206574
           03020100  07060504  0b0a0908  0f0e0d0c
           13121110  17161514  1b1a1918  1f1e1d1c
           00000001  09000000  4a000000  00000000

       After running 20 rounds (10 column rounds interleaved with 10
       "diagonal rounds"), the ChaCha state looks like this:

       ChaCha state after 20 rounds

           837778ab  e238d763  a67ae21e  5950bb2f
           c4f2d0c7  fc62bb2f  8fa018fc  3f5ec7b7
           335271c2  f29489f3  eabda8fc  82e46ebd
           d19c12b4  b04e16de  9e83d0cb  4e3c50a2

       Finally, we add the original state to the result (simple vector or
       matrix addition), giving this:

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       ChaCha state at the end of the ChaCha20 operation

           e4e7f110  15593bd1  1fdd0f50  c47120a3
           c7f4d1c7  0368c033  9aaa2204  4e6cd4c3
           466482d2  09aa9f07  05d7c214  a2028bd9
           d19c12b5  b94e16de  e883d0cb  4e3c50a2

       After we serialize the state, we get this:

      Serialized Block:
      000  10 f1 e7 e4 d1 3b 59 15 50 0f dd 1f a3 20 71 c4  .....;Y.P.... q.
      016  c7 d1 f4 c7 33 c0 68 03 04 22 aa 9a c3 d4 6c 4e  ....3.h.."....lN
      032  d2 82 64 46 07 9f aa 09 14 c2 d7 05 d9 8b 02 a2  ..dF............
      048  b5 12 9c d1 de 16 4e b9 cb d0 83 e8 a2 50 3c 4e  ......N......P<N

    2.4.  The ChaCha20 Encryption Algorithm

       ChaCha20 is a stream cipher designed by D. J. Bernstein.  It is a
       refinement of the Salsa20 algorithm, and it uses a 256-bit key.

       ChaCha20 successively calls the ChaCha20 block function, with the
       same key and nonce, and with successively increasing block counter
       parameters.  ChaCha20 then serializes the resulting state by writing
       the numbers in little-endian order, creating a keystream block.
       Concatenating the keystream blocks from the successive blocks forms a
       keystream.  The ChaCha20 function then performs an XOR of this
       keystream with the plaintext.  Alternatively, each keystream block
       can be XORed with a plaintext block before proceeding to create the
       next block, saving some memory.  There is no requirement for the
       plaintext to be an integral multiple of 512 bits.  If there is extra
       keystream from the last block, it is discarded.  Specific protocols
       MAY require that the plaintext and ciphertext have certain length.
       Such protocols need to specify how the plaintext is padded and how
       much padding it receives.

       The inputs to ChaCha20 are:

       o  A 256-bit key

       o  A 32-bit initial counter.  This can be set to any number, but will
          usually be zero or one.  It makes sense to use one if we use the
          zero block for something else, such as generating a one-time
          authenticator key as part of an AEAD algorithm.

       o  A 96-bit nonce.  In some protocols, this is known as the
          Initialization Vector.

       o  An arbitrary-length plaintext

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       The output is an encrypted message, or "ciphertext", of the same
       length.

       Decryption is done in the same way.  The ChaCha20 block function is
       used to expand the key into a keystream, which is XORed with the
       ciphertext giving back the plaintext.

    2.4.1.  The ChaCha20 Encryption Algorithm in Pseudocode

         chacha20_encrypt(key, counter, nonce, plaintext):
            for j = 0 upto floor(len(plaintext)/64)-1
               key_stream = chacha20_block(key, counter+j, nonce)
               block = plaintext[(j*64)..(j*64+63)]
               encrypted_message +=  block ^ key_stream
               end
            if ((len(plaintext) % 64) != 0)
               j = floor(len(plaintext)/64)
               key_stream = chacha20_block(key, counter+j, nonce)
               block = plaintext[(j*64)..len(plaintext)-1]
               encrypted_message += (block^key_stream)[0..len(plaintext)%64]
               end
            return encrypted_message
            end

    2.4.2.  Example and Test Vector for the ChaCha20 Cipher

       For a test vector, we will use the following inputs to the ChaCha20
       block function:

       o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
          14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.

       o  Nonce = (00:00:00:00:00:00:00:4a:00:00:00:00).

       o  Initial Counter = 1.

       We use the following for the plaintext.  It was chosen to be long
       enough to require more than one block, but not so long that it would
       make this example cumbersome (so, less than 3 blocks):

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      Plaintext Sunscreen:
      000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
      016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
      032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
      048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
      064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
      080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
      096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
      112  74 2e                                            t.

       The following figure shows four ChaCha state matrices:

       1.  First block as it is set up.

       2.  Second block as it is set up.  Note that these blocks are only
           two bits apart -- only the counter in position 12 is different.

       3.  Third block is the first block after the ChaCha20 block operation
           was applied.

       4.  Final block is the second block after the ChaCha20 block
           operation was applied.

       After that, we show the keystream.

       First block setup:
           61707865  3320646e  79622d32  6b206574
           03020100  07060504  0b0a0908  0f0e0d0c
           13121110  17161514  1b1a1918  1f1e1d1c
           00000001  00000000  4a000000  00000000

       Second block setup:
           61707865  3320646e  79622d32  6b206574
           03020100  07060504  0b0a0908  0f0e0d0c
           13121110  17161514  1b1a1918  1f1e1d1c
           00000002  00000000  4a000000  00000000

       First block after block operation:
           f3514f22  e1d91b40  6f27de2f  ed1d63b8
           821f138c  e2062c3d  ecca4f7e  78cff39e
           a30a3b8a  920a6072  cd7479b5  34932bed
           40ba4c79  cd343ec6  4c2c21ea  b7417df0

       Second block after block operation:
           9f74a669  410f633f  28feca22  7ec44dec
           6d34d426  738cb970  3ac5e9f3  45590cc4
           da6e8b39  892c831a  cdea67c1  2b7e1d90
           037463f3  a11a2073  e8bcfb88  edc49139

    Nir & Langley                 Informational                    [Page 13]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       Keystream:
       22:4f:51:f3:40:1b:d9:e1:2f:de:27:6f:b8:63:1d:ed:8c:13:1f:82:3d:2c:06
       e2:7e:4f:ca:ec:9e:f3:cf:78:8a:3b:0a:a3:72:60:0a:92:b5:79:74:cd:ed:2b
       93:34:79:4c:ba:40:c6:3e:34:cd:ea:21:2c:4c:f0:7d:41:b7:69:a6:74:9f:3f
       63:0f:41:22:ca:fe:28:ec:4d:c4:7e:26:d4:34:6d:70:b9:8c:73:f3:e9:c5:3a
       c4:0c:59:45:39:8b:6e:da:1a:83:2c:89:c1:67:ea:cd:90:1d:7e:2b:f3:63

       Finally, we XOR the keystream with the plaintext, yielding the
       ciphertext:

      Ciphertext Sunscreen:
      000  6e 2e 35 9a 25 68 f9 80 41 ba 07 28 dd 0d 69 81  n.5.%h..A..(..i.
      016  e9 7e 7a ec 1d 43 60 c2 0a 27 af cc fd 9f ae 0b  .~z..C`..'......
      032  f9 1b 65 c5 52 47 33 ab 8f 59 3d ab cd 62 b3 57  ..e.RG3..Y=..b.W
      048  16 39 d6 24 e6 51 52 ab 8f 53 0c 35 9f 08 61 d8  .9.$.QR..S.5..a.
      064  07 ca 0d bf 50 0d 6a 61 56 a3 8e 08 8a 22 b6 5e  ....P.jaV....".^
      080  52 bc 51 4d 16 cc f8 06 81 8c e9 1a b7 79 37 36  R.QM.........y76
      096  5a f9 0b bf 74 a3 5b e6 b4 0b 8e ed f2 78 5e 42  Z...t.[......x^B
      112  87 4d                                            .M

    2.5.  The Poly1305 Algorithm

       Poly1305 is a one-time authenticator designed by D. J. Bernstein.
       Poly1305 takes a 32-byte one-time key and a message and produces a
       16-byte tag.  This tag is used to authenticate the message.

       The original article ([Poly1305]) is titled "The Poly1305-AES
       message-authentication code", and the MAC function there requires a
       128-bit AES key, a 128-bit "additional key", and a 128-bit (non-
       secret) nonce.  AES is used there for encrypting the nonce, so as to
       get a unique (and secret) 128-bit string, but as the paper states,
       "There is nothing special about AES here.  One can replace AES with
       an arbitrary keyed function from an arbitrary set of nonces to
       16-byte strings."

       Regardless of how the key is generated, the key is partitioned into
       two parts, called "r" and "s".  The pair (r,s) should be unique, and
       MUST be unpredictable for each invocation (that is why it was
       originally obtained by encrypting a nonce), while "r" MAY be
       constant, but needs to be modified as follows before being used: ("r"
       is treated as a 16-octet little-endian number):

       o  r[3], r[7], r[11], and r[15] are required to have their top four
          bits clear (be smaller than 16)

       o  r[4], r[8], and r[12] are required to have their bottom two bits
          clear (be divisible by 4)

    Nir & Langley                 Informational                    [Page 14]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       The following sample code clamps "r" to be appropriate:

       /*
       Adapted from poly1305aes_test_clamp.c version 20050207
       D. J. Bernstein
       Public domain.
       */

       #include "poly1305aes_test.h"

       void poly1305aes_test_clamp(unsigned char r[16])
       {
         r[3] &= 15;
         r[7] &= 15;
         r[11] &= 15;
         r[15] &= 15;
         r[4] &= 252;
         r[8] &= 252;
         r[12] &= 252;
       }

       Where "&=" is the C language bitwise AND assignment operator.

       The "s" should be unpredictable, but it is perfectly acceptable to
       generate both "r" and "s" uniquely each time.  Because each of them
       is 128 bits, pseudorandomly generating them (see Section 2.6) is also
       acceptable.

       The inputs to Poly1305 are:

       o  A 256-bit one-time key

       o  An arbitrary length message

       The output is a 128-bit tag.

       First, the "r" value is clamped.

       Next, set the constant prime "P" be 2^130-5:
       3fffffffffffffffffffffffffffffffb.  Also set a variable "accumulator"
       to zero.

    Nir & Langley                 Informational                    [Page 15]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       Next, divide the message into 16-byte blocks.  The last one might be
       shorter:

       o  Read the block as a little-endian number.

       o  Add one bit beyond the number of octets.  For a 16-byte block,
          this is equivalent to adding 2^128 to the number.  For the shorter

          block, it can be 2^120, 2^112, or any power of two that is evenly
          divisible by 8, all the way down to 2^8.

       o  If the block is not 17 bytes long (the last block), pad it with
          zeros.  This is meaningless if you are treating the blocks as
          numbers.

       o  Add this number to the accumulator.

       o  Multiply by "r".

       o  Set the accumulator to the result modulo p.  To summarize: Acc =
          ((Acc+block)*r) % p.

       Finally, the value of the secret key "s" is added to the accumulator,
       and the 128 least significant bits are serialized in little-endian
       order to form the tag.

    2.5.1.  The Poly1305 Algorithms in Pseudocode

          clamp(r): r &= 0x0ffffffc0ffffffc0ffffffc0fffffff
          poly1305_mac(msg, key):
             r = le_bytes_to_num(key[0..15])
             clamp(r)
             s = le_bytes_to_num(key[16..31])
             a = 0  /* a is the accumulator */
             p = (1<<130)-5
             for i=1 upto ceil(msg length in bytes / 16)
                n = le_bytes_to_num(msg[((i-1)*16)..(i*16)] | [0x01])
                a += n
                a = (r * a) % p
                end
             a += s
             return num_to_16_le_bytes(a)
             end

    Nir & Langley                 Informational                    [Page 16]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    2.5.2.  Poly1305 Example and Test Vector

       For our example, we will dispense with generating the one-time key
       using AES, and assume that we got the following keying material:

       o  Key Material: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8:01:0
          3:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b

       o  s as an octet string:
          01:03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b

       o  s as a 128-bit number: 1bf54941aff6bf4afdb20dfb8a800301

       o  r before clamping: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8

       o  Clamped r as a number: 806d5400e52447c036d555408bed685

       For our message, we'll use a short text:

      Message to be Authenticated:
      000  43 72 79 70 74 6f 67 72 61 70 68 69 63 20 46 6f  Cryptographic Fo
      016  72 75 6d 20 52 65 73 65 61 72 63 68 20 47 72 6f  rum Research Gro
      032  75 70                                            up

       Since Poly1305 works in 16-byte chunks, the 34-byte message divides
       into three blocks.  In the following calculation, "Acc" denotes the
       accumulator and "Block" the current block:

       Block #1

       Acc = 00
       Block = 6f4620636968706172676f7470797243
       Block with 0x01 byte = 016f4620636968706172676f7470797243
       Acc + block = 016f4620636968706172676f7470797243
       (Acc+Block) * r =
            b83fe991ca66800489155dcd69e8426ba2779453994ac90ed284034da565ecf
       Acc = ((Acc+Block)*r) % P = 2c88c77849d64ae9147ddeb88e69c83fc

       Block #2

       Acc = 2c88c77849d64ae9147ddeb88e69c83fc
       Block = 6f7247206863726165736552206d7572
       Block with 0x01 byte = 016f7247206863726165736552206d7572
       Acc + block = 437febea505c820f2ad5150db0709f96e
       (Acc+Block) * r =
            21dcc992d0c659ba4036f65bb7f88562ae59b32c2b3b8f7efc8b00f78e548a26
       Acc = ((Acc+Block)*r) % P = 2d8adaf23b0337fa7cccfb4ea344b30de

    Nir & Langley                 Informational                    [Page 17]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       Last Block

       Acc = 2d8adaf23b0337fa7cccfb4ea344b30de
       Block = 7075
       Block with 0x01 byte = 017075
       Acc + block = 2d8adaf23b0337fa7cccfb4ea344ca153
       (Acc + Block) * r =
            16d8e08a0f3fe1de4fe4a15486aca7a270a29f1e6c849221e4a6798b8e45321f
       ((Acc + Block) * r) % P = 28d31b7caff946c77c8844335369d03a7

       Adding s, we get this number, and serialize if to get the tag:

       Acc + s = 2a927010caf8b2bc2c6365130c11d06a8

       Tag: a8:06:1d:c1:30:51:36:c6:c2:2b:8b:af:0c:01:27:a9

    2.6.  Generating the Poly1305 Key Using ChaCha20

       As said in Section 2.5, it is acceptable to generate the one-time
       Poly1305 key pseudorandomly.  This section defines such a method.

       To generate such a key pair (r,s), we will use the ChaCha20 block
       function described in Section 2.3.  This assumes that we have a
       256-bit session key specifically for the Message Authentication Code
       (MAC) function.  Any document that specifies the use of Poly1305 as a
       MAC algorithm for some protocol MUST specify that 256 bits are
       allocated for the integrity key.  Note that in the AEAD construction
       defined in Section 2.8, the same key is used for encryption and key
       generation.

       The method is to call the block function with the following
       parameters:

       o  The 256-bit session integrity key is used as the ChaCha20 key.

       o  The block counter is set to zero.

       o  The protocol will specify a 96-bit or 64-bit nonce.  This MUST be
          unique per invocation with the same key, so it MUST NOT be
          randomly generated.  A counter is a good way to implement this,
          but other methods, such as a Linear Feedback Shift Register (LFSR)
          are also acceptable.  ChaCha20 as specified here requires a 96-bit
          nonce.  So if the provided nonce is only 64-bit, then the first 32
          bits of the nonce will be set to a constant number.  This will
          usually be zero, but for protocols with multiple senders it may be
          different for each sender, but SHOULD be the same for all
          invocations of the function with the same key by a particular
          sender.

    Nir & Langley                 Informational                    [Page 18]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       After running the block function, we have a 512-bit state.  We take
       the first 256 bits of the serialized state, and use those as the one-
       time Poly1305 key: the first 128 bits are clamped and form "r", while
       the next 128 bits become "s".  The other 256 bits are discarded.

       Note that while many protocols have provisions for a nonce for
       encryption algorithms (often called Initialization Vectors, or IVs),
       they usually don't have such a provision for the MAC function.  In
       that case, the per-invocation nonce will have to come from somewhere
       else, such as a message counter.

    2.6.1.  Poly1305 Key Generation in Pseudocode

          poly1305_key_gen(key,nonce):
             counter = 0
             block = chacha20_block(key,counter,nonce)
             return block[0..31]
             end

    2.6.2.  Poly1305 Key Generation Test Vector

       For this example, we'll set:

      Key:
      000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
      016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

       Nonce:
       000  00 00 00 00 00 01 02 03 04 05 06 07              ............

       The ChaCha state setup with key, nonce, and block counter zero:
             61707865  3320646e  79622d32  6b206574
             83828180  87868584  8b8a8988  8f8e8d8c
             93929190  97969594  9b9a9998  9f9e9d9c
             00000000  00000000  03020100  07060504

       The ChaCha state after 20 rounds:
             8ba0d58a  cc815f90  27405081  7194b24a
             37b633a8  a50dfde3  e2b8db08  46a6d1fd
             7da03782  9183a233  148ad271  b46773d1
             3cc1875a  8607def1  ca5c3086  7085eb87

      Output bytes:
      000  8a d5 a0 8b 90 5f 81 cc 81 50 40 27 4a b2 94 71  ....._...P@'J..q
      016  a8 33 b6 37 e3 fd 0d a5 08 db b8 e2 fd d1 a6 46  .3.7...........F

       And that output is also the 32-byte one-time key used for Poly1305.

    Nir & Langley                 Informational                    [Page 19]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    2.7.  A Pseudorandom Function for Crypto Suites Based on ChaCha/Poly1305

       Some protocols, such as IKEv2 ([RFC7296]), require a Pseudorandom
       Function (PRF), mostly for key derivation.  In the IKEv2 definition,
       a PRF is a function that accepts a variable-length key and a
       variable-length input, and returns a fixed-length output.  Most
       commonly, Hashed MAC (HMAC) constructions are used for this purpose,
       and often the same function is used for both message authentication
       and PRF.

       Poly1305 is not a suitable choice for a PRF.  Poly1305 prohibits
       using the same key twice, whereas the PRF in IKEv2 is used multiple
       times with the same key.  Additionally, unlike HMAC, Poly1305 is
       biased, so using it for key derivation would reduce the security of
       the symmetric encryption.

       Chacha20 could be used as a key-derivation function, by generating an
       arbitrarily long keystream.  However, that is not what protocols such
       as IKEv2 require.

       For this reason, this document does not specify a PRF.

    2.8.  AEAD Construction

       AEAD_CHACHA20_POLY1305 is an authenticated encryption with additional
       data algorithm.  The inputs to AEAD_CHACHA20_POLY1305 are:

       o  A 256-bit key

       o  A 96-bit nonce -- different for each invocation with the same key

       o  An arbitrary length plaintext

       o  Arbitrary length additional authenticated data (AAD)

       Some protocols may have unique per-invocation inputs that are not 96
       bits in length.  For example, IPsec may specify a 64-bit nonce.  In
       such a case, it is up to the protocol document to define how to
       transform the protocol nonce into a 96-bit nonce, for example, by
       concatenating a constant value.

       The ChaCha20 and Poly1305 primitives are combined into an AEAD that
       takes a 256-bit key and 96-bit nonce as follows:

       o  First, a Poly1305 one-time key is generated from the 256-bit key
          and nonce using the procedure described in Section 2.6.

    Nir & Langley                 Informational                    [Page 20]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       o  Next, the ChaCha20 encryption function is called to encrypt the
          plaintext, using the same key and nonce, and with the initial
          counter set to 1.

       o  Finally, the Poly1305 function is called with the Poly1305 key
          calculated above, and a message constructed as a concatenation of
          the following:

          *  The AAD

          *  padding1 -- the padding is up to 15 zero bytes, and it brings
             the total length so far to an integral multiple of 16.  If the
             length of the AAD was already an integral multiple of 16 bytes,
             this field is zero-length.

          *  The ciphertext

          *  padding2 -- the padding is up to 15 zero bytes, and it brings
             the total length so far to an integral multiple of 16.  If the
             length of the ciphertext was already an integral multiple of 16
             bytes, this field is zero-length.

          *  The length of the additional data in octets (as a 64-bit
             little-endian integer).

          *  The length of the ciphertext in octets (as a 64-bit little-
             endian integer).

       The output from the AEAD is the concatenation of:

       o  A ciphertext of the same length as the plaintext.

       o  A 128-bit tag, which is the output of the Poly1305 function.

       Decryption is similar with the following differences:

       o  The roles of ciphertext and plaintext are reversed, so the
          ChaCha20 encryption function is applied to the ciphertext,
          producing the plaintext.

       o  The Poly1305 function is still run on the AAD and the ciphertext,
          not the plaintext.

       o  The calculated tag is bitwise compared to the received tag.  The
          message is authenticated if and only if the tags match.

    Nir & Langley                 Informational                    [Page 21]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       A few notes about this design:

       1.  The amount of encrypted data possible in a single invocation is
           2^32-1 blocks of 64 bytes each, because of the size of the block
           counter field in the ChaCha20 block function.  This gives a total
           of 274,877,906,880 bytes, or nearly 256 GB.  This should be
           enough for traffic protocols such as IPsec and TLS, but may be
           too small for file and/or disk encryption.  For such uses, we can
           return to the original design, reduce the nonce to 64 bits, and
           use the integer at position 13 as the top 32 bits of a 64-bit
           block counter, increasing the total message size to over a
           million petabytes (1,180,591,620,717,411,303,360 bytes to be
           exact).

       2.  Despite the previous item, the ciphertext length field in the
           construction of the buffer on which Poly1305 runs limits the
           ciphertext (and hence, the plaintext) size to 2^64 bytes, or
           sixteen thousand petabytes (18,446,744,073,709,551,616 bytes to
           be exact).

       The AEAD construction in this section is a novel composition of
       ChaCha20 and Poly1305.  A security analysis of this composition is
       given in [Procter].

       Here is a list of the parameters for this construction as defined in
       Section 4 of [RFC5116]:

       o  K_LEN (key length) is 32 octets.

       o  P_MAX (maximum size of the plaintext) is 274,877,906,880 bytes, or
          nearly 256 GB.

       o  A_MAX (maximum size of the associated data) is set to 2^64-1
          octets by the length field for associated data.

       o  N_MIN = N_MAX = 12 octets.

       o  C_MAX = P_MAX + tag length = 274,877,906,896 octets.

       Distinct AAD inputs (as described in Section 3.3 of [RFC5116]) shall
       be concatenated into a single input to AEAD_CHACHA20_POLY1305.  It is
       up to the application to create a structure in the AAD input if it is
       needed.

    Nir & Langley                 Informational                    [Page 22]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    2.8.1.  Pseudocode for the AEAD Construction

          pad16(x):
             if (len(x) % 16)==0
                then return NULL
                else return copies(0, 16-(len(x)%16))
             end

          chacha20_aead_encrypt(aad, key, iv, constant, plaintext):
             nonce = constant | iv
             otk = poly1305_key_gen(key, nonce)
             ciphertext = chacha20_encrypt(key, 1, nonce, plaintext)
             mac_data = aad | pad16(aad)
             mac_data |= ciphertext | pad16(ciphertext)
             mac_data |= num_to_8_le_bytes(aad.length)
             mac_data |= num_to_8_le_bytes(ciphertext.length)
             tag = poly1305_mac(mac_data, otk)
             return (ciphertext, tag)

    2.8.2.  Example and Test Vector for AEAD_CHACHA20_POLY1305

       For a test vector, we will use the following inputs to the
       AEAD_CHACHA20_POLY1305 function:

      Plaintext:
      000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
      016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
      032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
      048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
      064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
      080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
      096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
      112  74 2e                                            t.

       AAD:
       000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7              PQRS........

      Key:
      000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
      016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

       IV:
       000  40 41 42 43 44 45 46 47                          @ABCDEFG

       32-bit fixed-common part:
       000  07 00 00 00                                      ....

    Nir & Langley                 Informational                    [Page 23]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       Setup for generating Poly1305 one-time key (sender id=7):
           61707865  3320646e  79622d32  6b206574
           83828180  87868584  8b8a8988  8f8e8d8c
           93929190  97969594  9b9a9998  9f9e9d9c
           00000000  00000007  43424140  47464544

       After generating Poly1305 one-time key:
           252bac7b  af47b42d  557ab609  8455e9a4
           73d6e10a  ebd97510  7875932a  ff53d53e
           decc7ea2  b44ddbad  e49c17d1  d8430bc9
           8c94b7bc  8b7d4b4b  3927f67d  1669a432

      Poly1305 Key:
      000  7b ac 2b 25 2d b4 47 af 09 b6 7a 55 a4 e9 55 84  {.+%-.G...zU..U.
      016  0a e1 d6 73 10 75 d9 eb 2a 93 75 78 3e d5 53 ff  ...s.u..*.ux>.S.

      Poly1305 r =  455e9a4057ab6080f47b42c052bac7b
      Poly1305 s = ff53d53e7875932aebd9751073d6e10a

       keystream bytes:
       9f:7b:e9:5d:01:fd:40:ba:15:e2:8f:fb:36:81:0a:ae:
       c1:c0:88:3f:09:01:6e:de:dd:8a:d0:87:55:82:03:a5:
       4e:9e:cb:38:ac:8e:5e:2b:b8:da:b2:0f:fa:db:52:e8:
       75:04:b2:6e:be:69:6d:4f:60:a4:85:cf:11:b8:1b:59:
       fc:b1:c4:5f:42:19:ee:ac:ec:6a:de:c3:4e:66:69:78:
       8e:db:41:c4:9c:a3:01:e1:27:e0:ac:ab:3b:44:b9:cf:
       5c:86:bb:95:e0:6b:0d:f2:90:1a:b6:45:e4:ab:e6:22:
       15:38

      Ciphertext:
      000  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
      016  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
      032  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
      048  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
      064  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
      080  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
      096  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
      112  61 16                                            a.

    Nir & Langley                 Informational                    [Page 24]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      AEAD Construction for Poly1305:
      000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 00 00 00 00  PQRS............
      016  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
      032  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
      048  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
      064  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
      080  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
      096  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
      112  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
      128  61 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00  a...............
      144  0c 00 00 00 00 00 00 00 72 00 00 00 00 00 00 00  ........r.......

       Note the four zero bytes in line 000 and the 14 zero bytes in line
       128

       Tag:
       1a:e1:0b:59:4f:09:e2:6a:7e:90:2e:cb:d0:60:06:91

    3.  Implementation Advice

       Each block of ChaCha20 involves 16 move operations and one increment
       operation for loading the state, 80 each of XOR, addition and roll
       operations for the rounds, 16 more add operations and 16 XOR
       operations for protecting the plaintext.  Section 2.3 describes the
       ChaCha block function as "adding the original input words".  This
       implies that before starting the rounds on the ChaCha state, we copy
       it aside, only to add it in later.  This is correct, but we can save
       a few operations if we instead copy the state and do the work on the
       copy.  This way, for the next block you don't need to recreate the
       state, but only to increment the block counter.  This saves
       approximately 5.5% of the cycles.

       It is not recommended to use a generic big number library such as the
       one in OpenSSL for the arithmetic operations in Poly1305.  Such
       libraries use dynamic allocation to be able to handle an integer of
       any size, but that flexibility comes at the expense of performance as
       well as side-channel security.  More efficient implementations that
       run in constant time are available, one of them in D. J. Bernstein's
       own library, NaCl ([NaCl]).  A constant-time but not optimal approach
       would be to naively implement the arithmetic operations for 288-bit
       integers, because even a naive implementation will not exceed 2^288
       in the multiplication of (acc+block) and r.  An efficient constant-
       time implementation can be found in the public domain library
       poly1305-donna ([Poly1305_Donna]).

    Nir & Langley                 Informational                    [Page 25]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    4.  Security Considerations

       The ChaCha20 cipher is designed to provide 256-bit security.

       The Poly1305 authenticator is designed to ensure that forged messages
       are rejected with a probability of 1-(n/(2^102)) for a 16n-byte
       message, even after sending 2^64 legitimate messages, so it is
       SUF-CMA (strong unforgeability against chosen-message attacks) in the
       terminology of [AE].

       Proving the security of either of these is beyond the scope of this
       document.  Such proofs are available in the referenced academic
       papers ([ChaCha], [Poly1305], [LatinDances], [LatinDances2], and
       [Zhenqing2012]).

       The most important security consideration in implementing this
       document is the uniqueness of the nonce used in ChaCha20.  Counters
       and LFSRs are both acceptable ways of generating unique nonces, as is
       encrypting a counter using a block cipher with a 64-bit block size
       such as DES.  Note that it is not acceptable to use a truncation of a
       counter encrypted with block ciphers with 128-bit or 256-bit blocks,
       because such a truncation may repeat after a short time.

       Consequences of repeating a nonce: If a nonce is repeated, then both
       the one-time Poly1305 key and the keystream are identical between the
       messages.  This reveals the XOR of the plaintexts, because the XOR of
       the plaintexts is equal to the XOR of the ciphertexts.

       The Poly1305 key MUST be unpredictable to an attacker.  Randomly
       generating the key would fulfill this requirement, except that
       Poly1305 is often used in communications protocols, so the receiver
       should know the key.  Pseudorandom number generation such as by
       encrypting a counter is acceptable.  Using ChaCha with a secret key
       and a nonce is also acceptable.

       The algorithms presented here were designed to be easy to implement
       in constant time to avoid side-channel vulnerabilities.  The
       operations used in ChaCha20 are all additions, XORs, and fixed rolls.
       All of these can and should be implemented in constant time.  Access
       to offsets into the ChaCha state and the number of operations do not
       depend on any property of the key, eliminating the chance of
       information about the key leaking through the timing of cache misses.

       For Poly1305, the operations are addition, multiplication. and
       modulus, all on numbers with greater than 128 bits.  This can be done
       in constant time, but a naive implementation (such as using some
       generic big number library) will not be constant time.  For example,
       if the multiplication is performed as a separate operation from the

    Nir & Langley                 Informational                    [Page 26]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       modulus, the result will sometimes be under 2^256 and sometimes be
       above 2^256.  Implementers should be careful about timing side-
       channels for Poly1305 by using the appropriate implementation of
       these operations.

       Validating the authenticity of a message involves a bitwise
       comparison of the calculated tag with the received tag.  In most use
       cases, nonces and AAD contents are not "used up" until a valid
       message is received.  This allows an attacker to send multiple
       identical messages with different tags until one passes the tag
       comparison.  This is hard if the attacker has to try all 2^128
       possible tags one by one.  However, if the timing of the tag
       comparison operation reveals how long a prefix of the calculated and
       received tags is identical, the number of messages can be reduced
       significantly.  For this reason, with online protocols,
       implementation MUST use a constant-time comparison function rather
       than relying on optimized but insecure library functions such as the
       C language's memcmp().

       Additionally, any protocol using this algorithm MUST include the
       complete tag to minimize the opportunity for forgery.  Tag truncation
       MUST NOT be done.

    5.  IANA Considerations

       IANA has updated the entry in the "Authenticated Encryption with
       Associated Data (AEAD) Parameters" registry with 29 as the Numeric ID
       and "AEAD_CHACHA20_POLY1305" as the name to point to this document as
       its reference.

    6.  References

    6.1.  Normative References

       [ChaCha]   Bernstein, D., "ChaCha, a variant of Salsa20", January
                  2008, <http://cr.yp.to/chacha/chacha-20080128.pdf>.

       [Poly1305]
                  Bernstein, D., "The Poly1305-AES message-authentication
                  code", March 2005,
                  <http://cr.yp.to/mac/poly1305-20050329.pdf>.

       [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
                  Requirement Levels", BCP 14, RFC 2119,
                  DOI 10.17487/RFC2119, March 1997,
                  <https://www.rfc-editor.org/info/rfc2119>.

    Nir & Langley                 Informational                    [Page 27]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
                  2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
                  May 2017, <https://www.rfc-editor.org/info/rfc8174>.

    6.2.  Informative References

       [AE]       Bellare, M. and C. Namprempre, "Authenticated Encryption:
                  Relations among notions and analysis of the generic
                  composition paradigm", DOI 10.1007/s00145-008-9026-x,
                  September 2008,
                  <http://dl.acm.org/citation.cfm?id=1410269>.

       [Cache-Collisions]
                  Bonneau, J. and I. Mironov, "Cache-Collision Timing
                  Attacks Against AES", 2006,
                  <http://research.microsoft.com/pubs/64024/aes-timing.pdf>.

       [FIPS-197]
                  National Institute of Standards and Technology, "Advanced
                  Encryption Standard (AES)", FIPS PUB 197, November 2001,
                  <http://csrc.nist.gov/publications/fips/fips197/
                  fips-197.pdf>.

       [LatinDances]
                  Aumasson, J., Fischer, S., Khazaei, S., Meier, W., and C.
                  Rechberger, "New Features of Latin Dances: Analysis of
                  Salsa, ChaCha, and Rumba", December 2007,
                  <http://cr.yp.to/rumba20/newfeatures-20071218.pdf>.

       [LatinDances2]
                  Ishiguro, T., Kiyomoto, S., and Y. Miyake, "Modified
                  version of 'Latin Dances Revisited: New Analytic Results
                  of Salsa20 and ChaCha'", February 2012,
                  <https://eprint.iacr.org/2012/065.pdf>.

       [NaCl]     Bernstein, D., Lange, T., and P. Schwabe, "NaCl:
                  Networking and Cryptography library", July 2012,
                  <http://nacl.cr.yp.to>.

       [Poly1305_Donna]
                  "poly1305-donna", commit e6ad6e0, March 2016,
                  <https://github.com/floodyberry/poly1305-donna>.

       [Procter]  Procter, G., "A Security Analysis of the Composition of
                  ChaCha20 and Poly1305", August 2014,
                  <http://eprint.iacr.org/2014/613.pdf>.

    Nir & Langley                 Informational                    [Page 28]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
                  Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
                  <https://www.rfc-editor.org/info/rfc5116>.

       [RFC7296]  Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
                  Kivinen, "Internet Key Exchange Protocol Version 2
                  (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
                  2014, <https://www.rfc-editor.org/info/rfc7296>.

       [RFC7539]  Nir, Y. and A. Langley, "ChaCha20 and Poly1305 for IETF
                  Protocols", RFC 7539, DOI 10.17487/RFC7539, May 2015,
                  <https://www.rfc-editor.org/info/rfc7539>.

       [SP800-67]
                  National Institute of Standards and Technology,
                  "Recommendation for the Triple Data Encryption Algorithm
                  (TDEA) Block Cipher", NIST 800-67, Rev. 2, November 2017,
                  <https://csrc.nist.gov/publications/detail/sp/800-67/
                  rev-2/final>.

       [Standby-Cipher]
                  McGrew, D., Grieco, A., and Y. Sheffer, "Selection of
                  Future Cryptographic Standards", Work in Progress, draft-
                  mcgrew-standby-cipher-00, January 2013.

       [Zhenqing2012]
                  Zhenqing, S., Bin, Z., Dengguo, F., and W. Wenling,
                  "Improved Key Recovery Attacks on Reduced-Round Salsa20
                  and ChaCha*", 2012.

    Nir & Langley                 Informational                    [Page 29]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    Appendix A.  Additional Test Vectors

       The subsections of this appendix contain more test vectors for the
       algorithms in the subsections of Section 2.

    A.1.  The ChaCha20 Block Functions

      Test Vector #1:
      ==============

      Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 00              ............

      Block Counter = 0

        ChaCha state at the end
            ade0b876  903df1a0  e56a5d40  28bd8653
            b819d2bd  1aed8da0  ccef36a8  c70d778b
            7c5941da  8d485751  3fe02477  374ad8b8
            f4b8436a  1ca11815  69b687c3  8665eeb2

      Keystream:
      000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
      016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
      032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
      048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

      Test Vector #2:
      ==============

      Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 00              ............

      Block Counter = 1

        ChaCha state at the end
            bee7079f  7a385155  7c97ba98  0d082d73
            a0290fcb  6965e348  3e53c612  ed7aee32
            7621b729  434ee69c  b03371d5  d539d874
            281fed31  45fb0a51  1f0ae1ac  6f4d794b

    Nir & Langley                 Informational                    [Page 30]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Keystream:
      000  9f 07 e7 be 55 51 38 7a 98 ba 97 7c 73 2d 08 0d  ....UQ8z...|s-..
      016  cb 0f 29 a0 48 e3 65 69 12 c6 53 3e 32 ee 7a ed  ..).H.ei..S>2.z.
      032  29 b7 21 76 9c e6 4e 43 d5 71 33 b0 74 d8 39 d5  ).!v..NC.q3.t.9.
      048  31 ed 1f 28 51 0a fb 45 ac e1 0a 1f 4b 79 4d 6f  1..(Q..E....KyMo

      Test Vector #3:
      ==============

      Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 00              ............

      Block Counter = 1

        ChaCha state at the end
            2452eb3a  9249f8ec  8d829d9b  ddd4ceb1
            e8252083  60818b01  f38422b8  5aaa49c9
            bb00ca8e  da3ba7b4  c4b592d1  fdf2732f
            4436274e  2561b3c8  ebdd4aa6  a0136c00

      Keystream:
      000  3a eb 52 24 ec f8 49 92 9b 9d 82 8d b1 ce d4 dd  :.R$..I.........
      016  83 20 25 e8 01 8b 81 60 b8 22 84 f3 c9 49 aa 5a  . %....`."...I.Z
      032  8e ca 00 bb b4 a7 3b da d1 92 b5 c4 2f 73 f2 fd  ......;...../s..
      048  4e 27 36 44 c8 b3 61 25 a6 4a dd eb 00 6c 13 a0  N'6D..a%.J...l..

      Test Vector #4:
      ==============

      Key:
      000  00 ff 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 00              ............

      Block Counter = 2

        ChaCha state at the end
            fb4dd572  4bc42ef1  df922636  327f1394
            a78dea8f  5e269039  a1bebbc1  caf09aae
            a25ab213  48a6b46c  1b9d9bcb  092c5be6
            546ca624  1bec45d5  87f47473  96f0992e

    Nir & Langley                 Informational                    [Page 31]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Keystream:
      000  72 d5 4d fb f1 2e c4 4b 36 26 92 df 94 13 7f 32  r.M....K6&.....2
      016  8f ea 8d a7 39 90 26 5e c1 bb be a1 ae 9a f0 ca  ....9.&^........
      032  13 b2 5a a2 6c b4 a6 48 cb 9b 9d 1b e6 5b 2c 09  ..Z.l..H.....[,.
      048  24 a6 6c 54 d5 45 ec 1b 73 74 f4 87 2e 99 f0 96  $.lT.E..st......

      Test Vector #5:
      ==============

      Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 02              ............

      Block Counter = 0

        ChaCha state at the end
            374dc6c2  3736d58c  b904e24a  cd3f93ef
            88228b1a  96a4dfb3  5b76ab72  c727ee54
            0e0e978a  f3145c95  1b748ea8  f786c297
            99c28f5f  628314e8  398a19fa  6ded1b53

      Keystream:
      000  c2 c6 4d 37 8c d5 36 37 4a e2 04 b9 ef 93 3f cd  ..M7..67J.....?.
      016  1a 8b 22 88 b3 df a4 96 72 ab 76 5b 54 ee 27 c7  ..".....r.v[T.'.
      032  8a 97 0e 0e 95 5c 14 f3 a8 8e 74 1b 97 c2 86 f7  .....\....t.....
      048  5f 8f c2 99 e8 14 83 62 fa 19 8a 39 53 1b ed 6d  _......b...9S..m

    Nir & Langley                 Informational                    [Page 32]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    A.2.  ChaCha20 Encryption

      Test Vector #1:
      ==============

      Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 00              ............

      Initial Block Counter = 0

      Plaintext:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Ciphertext:
      000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
      016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
      032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
      048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

      Test Vector #2:
      ==============

      Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 02              ............

      Initial Block Counter = 1

    Nir & Langley                 Informational                    [Page 33]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Plaintext:
      000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
      016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
      032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
      048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
      064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
      080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
      096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
      112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
      128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
      144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
      160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
      176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
      192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
      208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
      224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
      240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
      256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
      272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
      288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
      304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
      320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
      336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
      352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
      368  73 73 65 64 20 74 6f                             ssed to

    Nir & Langley                 Informational                    [Page 34]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Ciphertext:
      000  a3 fb f0 7d f3 fa 2f de 4f 37 6c a2 3e 82 73 70  ...}../.O7l.>.sp
      016  41 60 5d 9f 4f 4f 57 bd 8c ff 2c 1d 4b 79 55 ec  A`].OOW...,.KyU.
      032  2a 97 94 8b d3 72 29 15 c8 f3 d3 37 f7 d3 70 05  *....r)....7..p.
      048  0e 9e 96 d6 47 b7 c3 9f 56 e0 31 ca 5e b6 25 0d  ....G...V.1.^.%.
      064  40 42 e0 27 85 ec ec fa 4b 4b b5 e8 ea d0 44 0e  @B.'....KK....D.
      080  20 b6 e8 db 09 d8 81 a7 c6 13 2f 42 0e 52 79 50   ........./B.RyP
      096  42 bd fa 77 73 d8 a9 05 14 47 b3 29 1c e1 41 1c  B..ws....G.)..A.
      112  68 04 65 55 2a a6 c4 05 b7 76 4d 5e 87 be a8 5a  h.eU*....vM^...Z
      128  d0 0f 84 49 ed 8f 72 d0 d6 62 ab 05 26 91 ca 66  ...I..r..b..&..f
      144  42 4b c8 6d 2d f8 0e a4 1f 43 ab f9 37 d3 25 9d  BK.m-....C..7.%.
      160  c4 b2 d0 df b4 8a 6c 91 39 dd d7 f7 69 66 e9 28  ......l.9...if.(
      176  e6 35 55 3b a7 6c 5c 87 9d 7b 35 d4 9e b2 e6 2b  .5U;.l\..{5....+
      192  08 71 cd ac 63 89 39 e2 5e 8a 1e 0e f9 d5 28 0f  .q..c.9.^.....(.
      208  a8 ca 32 8b 35 1c 3c 76 59 89 cb cf 3d aa 8b 6c  ..2.5.<vY...=..l
      224  cc 3a af 9f 39 79 c9 2b 37 20 fc 88 dc 95 ed 84  .:..9y.+7 ......
      240  a1 be 05 9c 64 99 b9 fd a2 36 e7 e8 18 b0 4b 0b  ....d....6....K.
      256  c3 9c 1e 87 6b 19 3b fe 55 69 75 3f 88 12 8c c0  ....k.;.Uiu?....
      272  8a aa 9b 63 d1 a1 6f 80 ef 25 54 d7 18 9c 41 1f  ...c..o..%T...A.
      288  58 69 ca 52 c5 b8 3f a3 6f f2 16 b9 c1 d3 00 62  Xi.R..?.o......b
      304  be bc fd 2d c5 bc e0 91 19 34 fd a7 9a 86 f6 e6  ...-.....4......
      320  98 ce d7 59 c3 ff 9b 64 77 33 8f 3d a4 f9 cd 85  ...Y...dw3.=....
      336  14 ea 99 82 cc af b3 41 b2 38 4d d9 02 f3 d1 ab  .......A.8M.....
      352  7a c6 1d d2 9c 6f 21 ba 5b 86 2f 37 30 e3 7c fd  z....o!.[./70.|.
      368  c4 fd 80 6c 22 f2 21                             ...l".!

      Test Vector #3:
      ==============

      Key:
      000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
      016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

      Nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 02              ............

      Initial Block Counter = 42

      Plaintext:
      000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
      016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
      032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
      048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
      064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
      080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
      096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
      112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

    Nir & Langley                 Informational                    [Page 35]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Ciphertext:
      000  62 e6 34 7f 95 ed 87 a4 5f fa e7 42 6f 27 a1 df  b.4....._..Bo'..
      016  5f b6 91 10 04 4c 0d 73 11 8e ff a9 5b 01 e5 cf  _....L.s....[...
      032  16 6d 3d f2 d7 21 ca f9 b2 1e 5f b1 4c 61 68 71  .m=..!...._.Lahq
      048  fd 84 c5 4f 9d 65 b2 83 19 6c 7f e4 f6 05 53 eb  ...O.e...l....S.
      064  f3 9c 64 02 c4 22 34 e3 2a 35 6b 3e 76 43 12 a6  ..d.."4.*5k>vC..
      080  1a 55 32 05 57 16 ea d6 96 25 68 f8 7d 3f 3f 77  .U2.W....%h.}??w
      096  04 c6 a8 d1 bc d1 bf 4d 50 d6 15 4b 6d a7 31 b1  .......MP..Km.1.
      112  87 b5 8d fd 72 8a fa 36 75 7a 79 7a c1 88 d1     ....r..6uzyz...

    A.3.  Poly1305 Message Authentication Code

       Notice how, in test vector #2, r is equal to zero.  The part of the
       Poly1305 algorithm where the accumulator is multiplied by r means
       that with r equal zero, the tag will be equal to s regardless of the
       content of the text.  Fortunately, all the proposed methods of
       generating r are such that getting this particular weak key is very
       unlikely.

      Test Vector #1:
      ==============

      One-time Poly1305 Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Text to MAC:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Tag:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      Test Vector #2:
      ==============

      One-time Poly1305 Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

    Nir & Langley                 Informational                    [Page 36]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Text to MAC:
      000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
      016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
      032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
      048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
      064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
      080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
      096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
      112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
      128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
      144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
      160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
      176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
      192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
      208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
      224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
      240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
      256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
      272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
      288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
      304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
      320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
      336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
      352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
      368  73 73 65 64 20 74 6f                             ssed to

      Tag:
      000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

      Test Vector #3:
      ==============

      One-time Poly1305 Key:
      000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

    Nir & Langley                 Informational                    [Page 37]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Text to MAC:
      000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
      016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
      032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
      048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
      064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
      080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
      096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
      112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
      128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
      144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
      160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
      176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
      192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
      208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
      224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
      240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
      256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
      272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
      288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
      304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
      320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
      336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
      352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
      368  73 73 65 64 20 74 6f                             ssed to

      Tag:
      000  f3 47 7e 7c d9 54 17 af 89 a6 b8 79 4c 31 0c f0  .G~|.T.....yL1..

    Nir & Langley                 Informational                    [Page 38]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Test Vector #4:
      ==============

      One-time Poly1305 Key:
      000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
      016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

      Text to MAC:
      000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
      016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
      032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
      048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
      064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
      080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
      096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
      112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

      Tag:
      000  45 41 66 9a 7e aa ee 61 e7 08 dc 7c bc c5 eb 62  EAf.~..a...|...b

       Test Vector #5: If one uses 130-bit partial reduction, does the code
       handle the case where partially reduced final result is not fully
       reduced?

       R:
       02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       S:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       data:
       FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
       tag:
       03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

       Test Vector #6: What happens if addition of s overflows modulo 2^128?

       R:
       02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       S:
       FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
       data:
       02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       tag:
       03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

    Nir & Langley                 Informational                    [Page 39]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       Test Vector #7: What happens if data limb is all ones and there is
       carry from lower limb?

       R:
       01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       S:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       data:
       FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
       F0 FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
       11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       tag:
       05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

       Test Vector #8: What happens if final result from polynomial part is
       exactly 2^130-5?

       R:
       01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       S:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       data:
       FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
       FB FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE
       01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
       tag:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

       Test Vector #9: What happens if final result from polynomial part is
       exactly 2^130-6?

       R:
       02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       S:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       data:
       FD FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
       tag:
       FA FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF

    Nir & Langley                 Informational                    [Page 40]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       Test Vector #10: What happens if 5*H+L-type reduction produces
       131-bit intermediate result?

       R:
       01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
       S:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       data:
       E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
       33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       tag:
       14 00 00 00 00 00 00 00 55 00 00 00 00 00 00 00

       Test Vector #11: What happens if 5*H+L-type reduction produces
       131-bit final result?

       R:
       01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
       S:
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       data:
       E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
       33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
       tag:
       13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

    A.4.  Poly1305 Key Generation Using ChaCha20

      Test Vector #1:
      ==============

      The ChaCha20 Key:
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

      The nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 00              ............

      Poly1305 one-time key:
      000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
      016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..

    Nir & Langley                 Informational                    [Page 41]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      Test Vector #2:
      ==============

      The ChaCha20 Key
      000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
      016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

      The nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 02              ............

      Poly1305 one-time key:
      000  ec fa 25 4f 84 5f 64 74 73 d3 cb 14 0d a9 e8 76  ..%O._dts......v
      016  06 cb 33 06 6c 44 7b 87 bc 26 66 dd e3 fb b7 39  ..3.lD{..&f....9

      Test Vector #3:
      ==============

      The ChaCha20 Key
      000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
      016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

      The nonce:
      000  00 00 00 00 00 00 00 00 00 00 00 02              ............

      Poly1305 one-time key:
      000  96 5e 3b c6 f9 ec 7e d9 56 08 08 f4 d2 29 f9 4b  .^;...~.V....).K
      016  13 7f f2 75 ca 9b 3f cb dd 59 de aa d2 33 10 ae  ...u..?..Y...3..

    A.5.  ChaCha20-Poly1305 AEAD Decryption

       Below we see decrypting a message.  We receive a ciphertext, a nonce,
       and a tag.  We know the key.  We will check the tag and then
       (assuming that it validates) decrypt the ciphertext.  In this
       particular protocol, we'll assume that there is no padding of the
       plaintext.

    Nir & Langley                 Informational                    [Page 42]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

      The ChaCha20 Key
      000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
      016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

      Ciphertext:
      000  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
      016  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
      032  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
      048  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
      064  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
      080  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
      096  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
      112  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
      128  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
      144  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
      160  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
      176  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
      192  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
      208  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
      224  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
      240  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
      256  a6 ad 5c b4 02 2b 02 70 9b                       ..\..+.p.

      The nonce:
      000  00 00 00 00 01 02 03 04 05 06 07 08              ............

      The AAD:
      000  f3 33 88 86 00 00 00 00 00 00 4e 91              .3........N.

      Received Tag:
      000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

    Nir & Langley                 Informational                    [Page 43]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       First, we calculate the one-time Poly1305 key

        ChaCha state with key setup
            61707865  3320646e  79622d32  6b206574
            a540921c  8ad355eb  868833f3  f0b5f604
            c1173947  09802b40  bc5cca9d  c0757020
            00000000  00000000  04030201  08070605

        ChaCha state after 20 rounds
            a94af0bd  89dee45c  b64bb195  afec8fa1
            508f4726  63f554c0  1ea2c0db  aa721526
            11b1e514  a0bacc0f  828a6015  d7825481
            e8a4a850  d9dcbbd6  4c2de33a  f8ccd912

       out bytes:
      bd:f0:4a:a9:5c:e4:de:89:95:b1:4b:b6:a1:8f:ec:af:
      26:47:8f:50:c0:54:f5:63:db:c0:a2:1e:26:15:72:aa

      Poly1305 one-time key:
      000  bd f0 4a a9 5c e4 de 89 95 b1 4b b6 a1 8f ec af  ..J.\.....K.....
      016  26 47 8f 50 c0 54 f5 63 db c0 a2 1e 26 15 72 aa  &G.P.T.c....&.r.

       Next, we construct the AEAD buffer

      Poly1305 Input:
      000  f3 33 88 86 00 00 00 00 00 00 4e 91 00 00 00 00  .3........N.....
      016  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
      032  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
      048  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
      064  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
      080  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
      096  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
      112  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
      128  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
      144  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
      160  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
      176  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
      192  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
      208  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
      224  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
      240  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
      256  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
      272  a6 ad 5c b4 02 2b 02 70 9b 00 00 00 00 00 00 00  ..\..+.p........
      288  0c 00 00 00 00 00 00 00 09 01 00 00 00 00 00 00  ................

    Nir & Langley                 Informational                    [Page 44]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

       We calculate the Poly1305 tag and find that it matches

      Calculated Tag:
      000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

       Finally, we decrypt the ciphertext

      Plaintext::
      000  49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 73 20  Internet-Drafts
      016  61 72 65 20 64 72 61 66 74 20 64 6f 63 75 6d 65  are draft docume
      032  6e 74 73 20 76 61 6c 69 64 20 66 6f 72 20 61 20  nts valid for a
      048  6d 61 78 69 6d 75 6d 20 6f 66 20 73 69 78 20 6d  maximum of six m
      064  6f 6e 74 68 73 20 61 6e 64 20 6d 61 79 20 62 65  onths and may be
      080  20 75 70 64 61 74 65 64 2c 20 72 65 70 6c 61 63   updated, replac
      096  65 64 2c 20 6f 72 20 6f 62 73 6f 6c 65 74 65 64  ed, or obsoleted
      112  20 62 79 20 6f 74 68 65 72 20 64 6f 63 75 6d 65   by other docume
      128  6e 74 73 20 61 74 20 61 6e 79 20 74 69 6d 65 2e  nts at any time.
      144  20 49 74 20 69 73 20 69 6e 61 70 70 72 6f 70 72   It is inappropr
      160  69 61 74 65 20 74 6f 20 75 73 65 20 49 6e 74 65  iate to use Inte
      176  72 6e 65 74 2d 44 72 61 66 74 73 20 61 73 20 72  rnet-Drafts as r
      192  65 66 65 72 65 6e 63 65 20 6d 61 74 65 72 69 61  eference materia
      208  6c 20 6f 72 20 74 6f 20 63 69 74 65 20 74 68 65  l or to cite the
      224  6d 20 6f 74 68 65 72 20 74 68 61 6e 20 61 73 20  m other than as
      240  2f e2 80 9c 77 6f 72 6b 20 69 6e 20 70 72 6f 67  /...work in prog
      256  72 65 73 73 2e 2f e2 80 9d                       ress./...

    Appendix B.  Performance Measurements of ChaCha20

       The following measurements were made by Adam Langley for a blog post
       published on February 27th, 2014.  The original blog post was
       available at the time of this writing at
       <https://www.imperialviolet.org/2014/02/27/tlssymmetriccrypto.html>.

         +----------------------------+-------------+-------------------+
         | Chip                       | AES-128-GCM | ChaCha20-Poly1305 |
         +----------------------------+-------------+-------------------+
         | OMAP 4460                  |  24.1 MB/s  |     75.3 MB/s     |
         | Snapdragon S4 Pro          |  41.5 MB/s  |     130.9 MB/s    |
         | Sandy Bridge Xeon (AES-NI) |   900 MB/s  |      500 MB/s     |
         +----------------------------+-------------+-------------------+

                             Table 1: Speed Comparison

    Nir & Langley                 Informational                    [Page 45]

    RFC 8439                   ChaCha20 & Poly1305                 June 2018

    Acknowledgements

       ChaCha20 and Poly1305 were invented by Daniel J. Bernstein.  The AEAD
       construction and the method of creating the one-time Poly1305 key
       were invented by Adam Langley.

       Thanks to Robert Ransom, Watson Ladd, Stefan Buhler, Dan Harkins, and
       Kenny Paterson for their helpful comments and explanations.  Thanks
       to Niels Moller for suggesting the more efficient AEAD construction
       in this document.  Special thanks to Ilari Liusvaara for providing
       extra test vectors, helpful comments, and for being the first to
       attempt an implementation from this document.  Thanks to Sean
       Parkinson for suggesting improvements to the examples and the
       pseudocode.  Thanks to David Ireland for pointing out a bug in the
       pseudocode, and to Stephen Farrell and Alyssa Rowan for pointing out
       missing advise in the security considerations.

       Special thanks goes to Gordon Procter for performing a security
       analysis of the composition and publishing [Procter].

       Jim Schaad and John Mattson provided feedback on tag truncation, and
       Russ Housley, Stanislav Smyshlyaev, and John Mattson each provided a
       review of this version.

    Authors' Addresses

       Yoav Nir
       Dell EMC
       9 Andrei Sakharov St
       Haifa  3190500
       Israel

       Email: ynir.ietf@gmail.com

       Adam Langley
       Google, Inc.

       Email: agl@google.com

    Nir & Langley                 Informational                    [Page 46]