idnits 2.17.1 

draft-irtf-cfrg-chacha20-poly1305-01.txt:

  Checking boilerplate required by RFC 5378 and the IETF Trust (see
  https://trustee.ietf.org/license-info):
  ----------------------------------------------------------------------------

     No issues found here.

  Checking nits according to https://www.ietf.org/id-info/1id-guidelines.txt:
  ----------------------------------------------------------------------------

     No issues found here.

  Checking nits according to https://www.ietf.org/id-info/checklist :
  ----------------------------------------------------------------------------

     No issues found here.

  Miscellaneous warnings:
  ----------------------------------------------------------------------------

  == The copyright year in the IETF Trust and authors Copyright Line does not
     match the current year

  == Line 231 has weird spacing: '...db886dc  c9a62...'

  == Line 281 has weird spacing: '...ccccccc  ccccc...'

  == Line 282 has weird spacing: '...kkkkkkk  kkkkk...'

  == Line 283 has weird spacing: '...kkkkkkk  kkkkk...'

  == Line 284 has weird spacing: '...bbbbbbb  nnnnn...'

  == (9 more instances...)

  -- The document date (August 25, 2014) is 3531 days in the past.  Is this
     intentional?

  -- Found something which looks like a code comment -- if you have code
     sections in the document, please surround them with '<CODE BEGINS>' and
     '<CODE ENDS>' lines.


  Checking references for intended status: Informational
  ----------------------------------------------------------------------------

  -- Looks like a reference, but probably isn't: '3' on line 508

  -- Looks like a reference, but probably isn't: '7' on line 509

  -- Looks like a reference, but probably isn't: '11' on line 510

  -- Looks like a reference, but probably isn't: '15' on line 511

  -- Looks like a reference, but probably isn't: '4' on line 512

  -- Looks like a reference, but probably isn't: '8' on line 513

  -- Looks like a reference, but probably isn't: '12' on line 514

  -- Looks like a reference, but probably isn't: '16' on line 506

  -- Obsolete informational reference (is this intentional?): RFC 5996
     (Obsoleted by RFC 7296)


     Summary: 0 errors (**), 0 flaws (~~), 7 warnings (==), 11 comments (--).

     Run idnits with the --verbose option for more detailed information about
     the items above.

--------------------------------------------------------------------------------


2	Network Working Group                                             Y. Nir
3	Internet-Draft                                               Check Point
4	Intended status: Informational                                A. Langley
5	Expires: February 26, 2015                                    Google Inc
6	                                                         August 25, 2014

8	                ChaCha20 and Poly1305 for IETF protocols
9	                  draft-irtf-cfrg-chacha20-poly1305-01

11	Abstract

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

18	   This document does not introduce any new crypto, but is meant to
19	   serve as a stable reference and an implementation guide.

21	Status of this Memo

23	   This Internet-Draft is submitted in full conformance with the
24	   provisions of BCP 78 and BCP 79.

26	   Internet-Drafts are working documents of the Internet Engineering
27	   Task Force (IETF).  Note that other groups may also distribute
28	   working documents as Internet-Drafts.  The list of current Internet-
29	   Drafts is at http://datatracker.ietf.org/drafts/current/.

31	   Internet-Drafts are draft documents valid for a maximum of six months
32	   and may be updated, replaced, or obsoleted by other documents at any
33	   time.  It is inappropriate to use Internet-Drafts as reference
34	   material or to cite them other than as "work in progress."

36	   This Internet-Draft will expire on February 26, 2015.

38	Copyright Notice

40	   Copyright (c) 2014 IETF Trust and the persons identified as the
41	   document authors.  All rights reserved.

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

50	Table of Contents

52	   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
53	     1.1.  Conventions Used in This Document  . . . . . . . . . . . .  3
54	   2.  The Algorithms . . . . . . . . . . . . . . . . . . . . . . . .  4
55	     2.1.  The ChaCha Quarter Round . . . . . . . . . . . . . . . . .  4
56	       2.1.1.  Test Vector for the ChaCha Quarter Round . . . . . . .  4
57	     2.2.  A Quarter Round on the ChaCha State  . . . . . . . . . . .  5
58	       2.2.1.  Test Vector for the Quarter Round on the ChaCha
59	               state  . . . . . . . . . . . . . . . . . . . . . . . .  5
60	     2.3.  The ChaCha20 block Function  . . . . . . . . . . . . . . .  6
61	       2.3.1.  Test Vector for the ChaCha20 Block Function  . . . . .  7
62	     2.4.  The ChaCha20 encryption algorithm  . . . . . . . . . . . .  8
63	       2.4.1.  Example and Test Vector for the ChaCha20 Cipher  . . .  9
64	     2.5.  The Poly1305 algorithm . . . . . . . . . . . . . . . . . . 11
65	       2.5.1.  Poly1305 Example and Test Vector . . . . . . . . . . . 13
66	     2.6.  Generating the Poly1305 key using ChaCha20 . . . . . . . . 14
67	       2.6.1.  Poly1305 Key Generation Test Vector  . . . . . . . . . 15
68	     2.7.  A Pseudo-Random Function for ChaCha/Poly-1305 based
69	           Crypto Suites  . . . . . . . . . . . . . . . . . . . . . . 16
70	     2.8.  AEAD Construction  . . . . . . . . . . . . . . . . . . . . 16
71	       2.8.1.  Example and Test Vector for AEAD_CHACHA20-POLY1305 . . 18
72	   3.  Implementation Advice  . . . . . . . . . . . . . . . . . . . . 20
73	   4.  Security Considerations  . . . . . . . . . . . . . . . . . . . 20
74	   5.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 21
75	   6.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 21
76	   7.  Changes from Previous Versions . . . . . . . . . . . . . . . . 22
77	     7.1.  Changes from version -00 to version -01  . . . . . . . . . 22
78	     7.2.  Changes from draft-nir-cfrg to draft-irtf-cfrg . . . . . . 22
79	   8.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 22
80	     8.1.  Normative References . . . . . . . . . . . . . . . . . . . 22
81	     8.2.  Informative References . . . . . . . . . . . . . . . . . . 22
82	   Appendix A.  Additional Test Vectors . . . . . . . . . . . . . . . 23
83	     A.1.  The ChaCha20 Block Functions . . . . . . . . . . . . . . . 24
84	     A.2.  ChaCha20 Encryption  . . . . . . . . . . . . . . . . . . . 27
85	     A.3.  Poly1305 Message Authentication Code . . . . . . . . . . . 29
86	     A.4.  Poly1305 Key Generation Using ChaCha20 . . . . . . . . . . 35
87	     A.5.  ChaCha20-Poly1305 AEAD Decryption  . . . . . . . . . . . . 36
88	   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 39

90	1.  Introduction

92	   The Advanced Encryption Standard (AES - [FIPS-197]) has become the
93	   gold standard in encryption.  Its efficient design, wide
94	   implementation, and hardware support allow for high performance in
95	   many areas.  On most modern platforms, AES is anywhere from 4x to 10x
96	   as fast as the previous most-used cipher, 3-key Data Encryption
97	   Standard (3DES - [FIPS-46]), which makes it not only the best choice,
98	   but the only practical choice.

100	   The problem is that if future advances in cryptanalysis reveal a
101	   weakness in AES, users will be in an unenviable position.  With the
102	   only other widely supported cipher being the much slower 3DES, it is
103	   not feasible to re-configure implementations to use 3DES.
104	   [standby-cipher] describes this issue and the need for a standby
105	   cipher in greater detail.

107	   This document defines such a standby cipher.  We use ChaCha20
108	   ([chacha]) with or without the Poly1305 ([poly1305]) authenticator.
109	   These algorithms are not just fast.  They are fast even in software-
110	   only C-language implementations, allowing for much quicker deployment
111	   when compared with algorithms such as AES that are significantly
112	   accelerated by hardware implementations.

114	   This document does not introduce these new algorithms.  They have
115	   been defined in scientific papers by D. J. Bernstein, which are
116	   referenced by this document.  The purpose of this document is to
117	   serve as a stable reference for IETF documents making use of these
118	   algorithms.

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

124	1.1.  Conventions Used in This Document

126	   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
127	   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
128	   document are to be interpreted as described in [RFC2119].

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

138	      0   1   2   3
139	      4   5   6   7
140	      8   9  10  11
141	     12  13  14  15

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

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

151	2.  The Algorithms

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

156	2.1.  The ChaCha Quarter Round

158	   The basic operation of the ChaCha algorithm is the quarter round.  It
159	   operates on four 32-bit unsigned integers, denoted a, b, c, and d.
160	   The operation is as follows (in C-like notation):
161	   o  a += b; d ^= a; d <<<= 16;
162	   o  c += d; b ^= c; b <<<= 12;
163	   o  a += b; d ^= a; d <<<= 8;
164	   o  c += d; b ^= c; b <<<= 7;
165	   Where "+" denotes integer addition modulo 2^32, "^" denotes a bitwise
166	   XOR, and "<<< n" denotes an n-bit left rotation (towards the high
167	   bits).

169	   For example, let's see the add, XOR and roll operations from the
170	   first line with sample numbers:
171	   o  b = 0x01020304
172	   o  a = 0x11111111
173	   o  d = 0x01234567
174	   o  a = a + b = 0x11111111 + 0x01020304 = 0x12131415
175	   o  d = d ^ a = 0x01234567 ^ 0x12131415 = 0x13305172
176	   o  d = d<<<16 = 0x51721330

178	2.1.1.  Test Vector for the ChaCha Quarter Round

180	   For a test vector, we will use the same numbers as in the example,
181	   adding something random for c.
182	   o  a = 0x11111111
183	   o  b = 0x01020304
184	   o  c = 0x9b8d6f43
185	   o  d = 0x01234567

187	   After running a Quarter Round on these 4 numbers, we get these:
188	   o  a = 0xea2a92f4
189	   o  b = 0xcb1cf8ce
190	   o  c = 0x4581472e
191	   o  d = 0x5881c4bb

193	2.2.  A Quarter Round on the ChaCha State

195	   The ChaCha state does not have 4 integer numbers, but 16.  So the
196	   quarter round operation works on only 4 of them - hence the name.
197	   Each quarter round operates on 4 pre-determined numbers in the ChaCha
198	   state.  We will denote by QUATERROUND(x,y,z,w) a quarter-round
199	   operation on the numbers at indexes x, y, z, and w of the ChaCha
200	   state when viewed as a vector.  For example, if we apply
201	   QUARTERROUND(1,5,9,13) to a state, this means running the quarter
202	   round operation on the elements marked with an asterisk, while
203	   leaving the others alone:

205	      0  *a   2   3
206	      4  *b   6   7
207	      8  *c  10  11
208	     12  *d  14  15

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

213	2.2.1.  Test Vector for the Quarter Round on the ChaCha state

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

218	   Sample ChaCha State

220	       879531e0  c5ecf37d  516461b1  c9a62f8a
221	       44c20ef3  3390af7f  d9fc690b  2a5f714c
222	       53372767  b00a5631  974c541a  359e9963
223	       5c971061  3d631689  2098d9d6  91dbd320

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

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

231	       879531e0  c5ecf37d  bdb886dc  c9a62f8a
232	       44c20ef3  3390af7f  d9fc690b  cfacafd2
233	       e46bea80  b00a5631  974c541a  359e9963
234	       5c971061  ccc07c79  2098d9d6  91dbd320

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

238	2.3.  The ChaCha20 block Function

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

243	   The inputs to ChaCha20 are:
244	   o  A 256-bit key, treated as a concatenation of 8 32-bit little-
245	      endian integers.
246	   o  A 96-bit nonce, treated as a concatenation of 3 32-bit little-
247	      endian integers.
248	   o  A 32-bit block count parameter, treated as a 32-bit little-endian
249	      integer.

251	   The output is 64 random-looking bytes.

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

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

268	   The ChaCha20 state is initialized as follows:
269	   o  The first 4 words (0-3) are constants: 0x61707865, 0x3320646e,
270	      0x79622d32, 0x6b206574.
271	   o  The next 8 words (4-11) are taken from the 256-bit key by reading
272	      the bytes in little-endian order, in 4-byte chunks.
273	   o  Word 12 is a block counter.  Since each block is 64-byte, a 32-bit
274	      word is enough for 256 Gigabytes of data.

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

281	       cccccccc  cccccccc  cccccccc  cccccccc
282	       kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
283	       kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
284	       bbbbbbbb  nnnnnnnn  nnnnnnnn  nnnnnnnn

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

288	   ChaCha20 runs 20 rounds, alternating between "column" and "diagonal"
289	   rounds.  Each round is 4 quarter-rounds, and they are run as follows.
290	   Quarter-rounds 1-4 are part of a "column" round, while 5-8 are part
291	   of a "diagonal" round:
292	   1.  QUARTERROUND ( 0, 4, 8,12)
293	   2.  QUARTERROUND ( 1, 5, 9,13)
294	   3.  QUARTERROUND ( 2, 6,10,14)
295	   4.  QUARTERROUND ( 3, 7,11,15)
296	   5.  QUARTERROUND ( 0, 5,10,15)
297	   6.  QUARTERROUND ( 1, 6,11,12)
298	   7.  QUARTERROUND ( 2, 7, 8,13)
299	   8.  QUARTERROUND ( 3, 4, 9,14)

301	   At the end of 20 rounds, we add the original input words to the
302	   output words, and serialize the result by sequencing the words one-
303	   by-one in little-endian order.

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

308	2.3.1.  Test Vector for the ChaCha20 Block Function

310	   For a test vector, we will use the following inputs to the ChaCha20
311	   block function:
312	   o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
313	      14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.  The key is a sequence of
314	      octets with no particular structure before we copy it into the
315	      ChaCha state.
316	   o  Nonce = (00:00:00:09:00:00:00:4a:00:00:00:00)
317	   o  Block Count = 1.

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

321	   ChaCha State with the key set up.

323	       61707865  3320646e  79622d32  6b206574
324	       03020100  07060504  0b0a0908  0f0e0d0c
325	       13121110  17161514  1b1a1918  1f1e1d1c
326	       00000001  09000000  4a000000  00000000

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

331	   ChaCha State after 20 rounds

333	       837778ab  e238d763  a67ae21e  5950bb2f
334	       c4f2d0c7  fc62bb2f  8fa018fc  3f5ec7b7
335	       335271c2  f29489f3  eabda8fc  82e46ebd
336	       d19c12b4  b04e16de  9e83d0cb  4e3c50a2

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

341	   ChaCha State at the end of the ChaCha20 operation

343	       e4e7f110  15593bd1  1fdd0f50  c47120a3
344	       c7f4d1c7  0368c033  9aaa2204  4e6cd4c3
345	       466482d2  09aa9f07  05d7c214  a2028bd9
346	       d19c12b5  b94e16de  e883d0cb  4e3c50a2

348	   After we serialize the state, we get this:

350	  Serialized Block:
351	  000  10 f1 e7 e4 d1 3b 59 15 50 0f dd 1f a3 20 71 c4  .....;Y.P.... q.
352	  016  c7 d1 f4 c7 33 c0 68 03 04 22 aa 9a c3 d4 6c 4e  ....3.h.."....lN
353	  032  d2 82 64 46 07 9f aa 09 14 c2 d7 05 d9 8b 02 a2  ..dF............
354	  048  b5 12 9c d1 de 16 4e b9 cb d0 83 e8 a2 50 3c 4e  ......N......P<N

356	2.4.  The ChaCha20 encryption algorithm

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

361	   ChaCha20 successively calls the ChaCha20 block function, with the
362	   same key and nonce, and with successively increasing block counter
363	   parameters.  ChaCha20 then serializes the resulting state by writing
364	   the numbers in little-endian order, creating a key-stream block.
365	   Concatenating the key-stream blocks from the successive blocks forms
366	   a key stream, which is then XOR-ed with the plaintext.
367	   Alternatively, each key-stream block can be XOR-ed with a plaintext
368	   block before proceeding to create the next block, saving some memory.

370	   There is no requirement for the plaintext to be an integral multiple
371	   of 512-bits.  If there is extra keystream from the last block, it is
372	   discarded.  Specific protocols MAY require that the plaintext and
373	   ciphertext have certain length.  Such protocols need to specify how
374	   the plaintext is padded, and how much padding it receives.

376	   The inputs to ChaCha20 are:
377	   o  A 256-bit key
378	   o  A 32-bit initial counter.  This can be set to any number, but will
379	      usually be zero or one.  It makes sense to use 1 if we use the
380	      zero block for something else, such as generating a one-time
381	      authenticator key as part of an AEAD algorithm.
382	   o  A 96-bit nonce.  In some protocols, this is known as the
383	      Initialization Vector.
384	   o  An arbitrary-length plaintext

386	   The output is an encrypted message of the same length.

388	   Decryption is done in the same way.  The ChaCha20 block function is
389	   used to expand the key into a key stream, which is XOR-ed with the
390	   ciphertext giving back the plaintext.

392	2.4.1.  Example and Test Vector for the ChaCha20 Cipher

394	   For a test vector, we will use the following inputs to the ChaCha20
395	   block function:
396	   o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
397	      14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.
398	   o  Nonce = (00:00:00:00:00:00:00:4a:00:00:00:00).
399	   o  Initial Counter = 1.

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

405	  Plaintext Sunscreen:
406	  000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
407	  016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
408	  032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
409	  048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
410	  064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
411	  080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
412	  096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
413	  112  74 2e                                            t.

415	   The following figure shows 4 ChaCha state matrices:

417	   1.  First block as it is set up.
418	   2.  Second block as it is set up.  Note that these blocks are only
419	       two bits apart - only the counter in position 12 is different.
420	   3.  Third block is the first block after the ChaCha20 block
421	       operation.
422	   4.  Final block is the second block after the ChaCha20 block
423	       operation was applied.
424	   After that, we show the keystream.

426	   First block setup:
427	       61707865  3320646e  79622d32  6b206574
428	       03020100  07060504  0b0a0908  0f0e0d0c
429	       13121110  17161514  1b1a1918  1f1e1d1c
430	       00000001  00000000  4a000000  00000000

432	   Second block setup:
433	       61707865  3320646e  79622d32  6b206574
434	       03020100  07060504  0b0a0908  0f0e0d0c
435	       13121110  17161514  1b1a1918  1f1e1d1c
436	       00000002  00000000  4a000000  00000000

438	   First block after block operation:
439	       f3514f22  e1d91b40  6f27de2f  ed1d63b8
440	       821f138c  e2062c3d  ecca4f7e  78cff39e
441	       a30a3b8a  920a6072  cd7479b5  34932bed
442	       40ba4c79  cd343ec6  4c2c21ea  b7417df0

444	   Second block after block operation:
445	       9f74a669  410f633f  28feca22  7ec44dec
446	       6d34d426  738cb970  3ac5e9f3  45590cc4
447	       da6e8b39  892c831a  cdea67c1  2b7e1d90
448	       037463f3  a11a2073  e8bcfb88  edc49139

450	   Keystream:
451	   22:4f:51:f3:40:1b:d9:e1:2f:de:27:6f:b8:63:1d:ed:8c:13:1f:82:3d:2c:06
452	   e2:7e:4f:ca:ec:9e:f3:cf:78:8a:3b:0a:a3:72:60:0a:92:b5:79:74:cd:ed:2b
453	   93:34:79:4c:ba:40:c6:3e:34:cd:ea:21:2c:4c:f0:7d:41:b7:69:a6:74:9f:3f
454	   63:0f:41:22:ca:fe:28:ec:4d:c4:7e:26:d4:34:6d:70:b9:8c:73:f3:e9:c5:3a
455	   c4:0c:59:45:39:8b:6e:da:1a:83:2c:89:c1:67:ea:cd:90:1d:7e:2b:f3:63

457	   Finally, we XOR the Keystream with the plaintext, yielding the
458	   Ciphertext:

460	  Ciphertext Sunscreen:
461	  000  6e 2e 35 9a 25 68 f9 80 41 ba 07 28 dd 0d 69 81  n.5.%h..A..(..i.
462	  016  e9 7e 7a ec 1d 43 60 c2 0a 27 af cc fd 9f ae 0b  .~z..C`..'......
463	  032  f9 1b 65 c5 52 47 33 ab 8f 59 3d ab cd 62 b3 57  ..e.RG3..Y=..b.W
464	  048  16 39 d6 24 e6 51 52 ab 8f 53 0c 35 9f 08 61 d8  .9.$.QR..S.5..a.
465	  064  07 ca 0d bf 50 0d 6a 61 56 a3 8e 08 8a 22 b6 5e  ....P.jaV....".^
466	  080  52 bc 51 4d 16 cc f8 06 81 8c e9 1a b7 79 37 36  R.QM.........y76
467	  096  5a f9 0b bf 74 a3 5b e6 b4 0b 8e ed f2 78 5e 42  Z...t.[......x^B
468	  112  87 4d                                            .M

470	2.5.  The Poly1305 algorithm

472	   Poly1305 is a one-time authenticator designed by D. J. Bernstein.
473	   Poly1305 takes a 32-byte one-time key and a message and produces a
474	   16-byte tag.

476	   The original article ([poly1305]) is entitled "The Poly1305-AES
477	   message-authentication code", and the MAC function there requires a
478	   128-bit AES key, a 128-bit "additional key", and a 128-bit (non-
479	   secret) nonce.  AES is used there for encrypting the nonce, so as to
480	   get a unique (and secret) 128-bit string, but as the paper states,
481	   "There is nothing special about AES here.  One can replace AES with
482	   an arbitrary keyed function from an arbitrary set of nonces to 16-
483	   byte strings."

485	   Regardless of how the key is generated, the key is partitioned into
486	   two parts, called "r" and "s".  The pair (r,s) should be unique, and
487	   MUST be unpredictable for each invocation (that is why it was
488	   originally obtained by encrypting a nonce), while "r" MAY be
489	   constant, but needs to be modified as follows before being used: ("r"
490	   is treated as a 16-octet little-endian number):
491	   o  r[3], r[7], r[11], and r[15] are required to have their top four
492	      bits clear (be smaller than 16)
493	   o  r[4], r[8], and r[12] are required to have their bottom two bits
494	      clear (be divisible by 4)

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

498	   /*
499	   Adapted from poly1305aes_test_clamp.c version 20050207
500	   D. J. Bernstein
501	   Public domain.
502	   */

504	   #include "poly1305aes_test.h"

506	   void poly1305aes_test_clamp(unsigned char r[16])
507	   {
508	     r[3] &= 15;
509	     r[7] &= 15;
510	     r[11] &= 15;
511	     r[15] &= 15;
512	     r[4] &= 252;
513	     r[8] &= 252;
514	     r[12] &= 252;
515	   }

517	   The "s" should be unpredictable, but it is perfectly acceptable to
518	   generate both "r" and "s" uniquely each time.  Because each of them
519	   is 128-bit, pseudo-randomly generating them (see Section 2.6) is also
520	   acceptable.

522	   The inputs to Poly1305 are:
523	   o  A 256-bit one-time key
524	   o  An arbitrary length message

526	   The output is a 128-bit tag.

528	   First, the "r" value should be clamped.

530	   Next, set the constant prime "P" be 2^130-5:
531	   3fffffffffffffffffffffffffffffffb.  Also set a variable "accumulator"
532	   to zero.

534	   Next, divide the message into 16-byte blocks.  The last one might be
535	   shorter:
536	   o  Read the block as a little-endian number.
537	   o  Add one bit beyond the number of octets.  For a 16-byte block this
538	      is equivalent to adding 2^128 to the number.  For the shorter
539	      block it can be 2^120, 2^112, or any power of two that is evenly
540	      divisible by 8, all the way down to 2^8.
541	   o  If the block is not 17 bytes long (the last block), pad it with
542	      zeros.  This is meaningless if you're treating it them as numbers.
543	   o  Add this number to the accumulator.

545	   o  Multiply by "r"
546	   o  Set the accumulator to the result modulo p.  To summarize: Acc =
547	      ((Acc+block)*r) % p.

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

553	2.5.1.  Poly1305 Example and Test Vector

555	   For our example, we will dispense with generating the one-time key
556	   using AES, and assume that we got the following keying material:
557	   o  Key Material: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8:01:
558	      03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b
559	   o  s as an octet string: 01:03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:
560	      f5:1b
561	   o  s as a 128-bit number: 1bf54941aff6bf4afdb20dfb8a800301
562	   o  r before clamping: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8
563	   o  Clamped r as a number: 806d5400e52447c036d555408bed685.

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

567	  Message to be Authenticated:
568	  000  43 72 79 70 74 6f 67 72 61 70 68 69 63 20 46 6f  Cryptographic Fo
569	  016  72 75 6d 20 52 65 73 65 61 72 63 68 20 47 72 6f  rum Research Gro
570	  032  75 70                                            up

572	   Since Poly1305 works in 16-byte chunks, the 34-byte message divides
573	   into 3 blocks.  In the following calculation, "Acc" denotes the
574	   accumulator and "Block" the current block:

576	   Block #1

578	   Acc = 00
579	   Block = 6f4620636968706172676f7470797243
580	   Block with 0x01 byte = 016f4620636968706172676f7470797243
581	   Acc + block = 016f4620636968706172676f7470797243
582	   (Acc+Block) * r =
583	        b83fe991ca66800489155dcd69e8426ba2779453994ac90ed284034da565ecf
584	   Acc = ((Acc+Block)*r) % P = 2c88c77849d64ae9147ddeb88e69c83fc
585	   Block #2

587	   Acc = 2c88c77849d64ae9147ddeb88e69c83fc
588	   Block = 6f7247206863726165736552206d7572
589	   Block with 0x01 byte = 016f7247206863726165736552206d7572
590	   Acc + block = 437febea505c820f2ad5150db0709f96e
591	   (Acc+Block) * r =
592	        21dcc992d0c659ba4036f65bb7f88562ae59b32c2b3b8f7efc8b00f78e548a26
593	   Acc = ((Acc+Block)*r) % P = 2d8adaf23b0337fa7cccfb4ea344b30de

595	   Last Block

597	   Acc = 2d8adaf23b0337fa7cccfb4ea344b30de
598	   Block = 7075
599	   Block with 0x01 byte = 017075
600	   Acc + block = 2d8adaf23b0337fa7cccfb4ea344ca153
601	   (Acc + Block) * r =
602	        16d8e08a0f3fe1de4fe4a15486aca7a270a29f1e6c849221e4a6798b8e45321f
603	   ((Acc + Block) * r) % P = 28d31b7caff946c77c8844335369d03a7

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

607	   Acc + s = 2a927010caf8b2bc2c6365130c11d06a8

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

611	2.6.  Generating the Poly1305 key using ChaCha20

613	   As said in Section 2.5, it is acceptable to generate the one-time
614	   Poly1305 pseudo-randomly.  This section proposes such a method.

616	   To generate such a key pair (r,s), we will use the ChaCha20 block
617	   function described in Section 2.3.  This assumes that we have a 256-
618	   bit session key for the MAC function, such as SK_ai and SK_ar in
619	   IKEv2 ([RFC5996]), the integrity key in ESP and AH, or the
620	   client_write_MAC_key and server_write_MAC_key in TLS.  Any document
621	   that specifies the use of Poly1305 as a MAC algorithm for some
622	   protocol must specify that 256 bits are allocated for the integrity
623	   key.  Note that in the AEAD construction defined in Section 2.8, the
624	   same key is used for encryption and key generation, so the use of
625	   SK_a* or *_write_MAC_key is only for stand-alone Poly1305.

627	   The method is to call the block function with the following
628	   parameters:
629	   o  The 256-bit session integrity key is used as the ChaCha20 key.
630	   o  The block counter is set to zero.

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

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

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

655	2.6.1.  Poly1305 Key Generation Test Vector

657	   For this example, we'll set:

659	  Key:
660	  000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
661	  016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

663	   Nonce:
664	   000  00 00 00 00 00 01 02 03 04 05 06 07              ............

666	   The ChaCha state set up with key, nonce, and block counter zero:
667	         61707865  3320646e  79622d32  6b206574
668	         83828180  87868584  8b8a8988  8f8e8d8c
669	         93929190  97969594  9b9a9998  9f9e9d9c
670	         00000000  00000000  03020100  07060504

672	   The ChaCha state after 20 rounds:
673	         8ba0d58a  cc815f90  27405081  7194b24a
674	         37b633a8  a50dfde3  e2b8db08  46a6d1fd
675	         7da03782  9183a233  148ad271  b46773d1
676	         3cc1875a  8607def1  ca5c3086  7085eb87

678	  Output bytes:
679	  000  8a d5 a0 8b 90 5f 81 cc 81 50 40 27 4a b2 94 71  ....._...P@'J..q
680	  016  a8 33 b6 37 e3 fd 0d a5 08 db b8 e2 fd d1 a6 46  .3.7...........F

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

684	2.7.  A Pseudo-Random Function for ChaCha/Poly-1305 based Crypto Suites

686	   Some protocols such as IKEv2([RFC5996]) require a Pseudo-Random
687	   Function (PRF), mostly for key derivation.  In the IKEv2 definition,
688	   a PRF is a function that accepts a variable-length key and a
689	   variable-length input, and returns a fixed-length output.  This
690	   section does not specify such a function.

692	   Poly-1305 is an obvious choice, because MAC functions are often used
693	   as PRFs.  However, Poly-1305 prohibits using the same key twice,
694	   whereas the PRF in IKEv2 is used multiple times with the same key.
695	   Adding a nonce or a counter to Poly-1305 can solve this issue, much
696	   as we do when using this function as a MAC, but that would require
697	   changing the interface for the PRF function.

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

703	   For this reason, this document does not specify a PRF, and recommends
704	   that crypto suites use some other PRF such as PRF_HMAC_SHA2_256
705	   (section 2.1.2 of [RFC4868])

707	2.8.  AEAD Construction

709	   AEAD_CHACHA20-POLY1305 is an authenticated encryption with additional
710	   data algorithm.  The inputs to AEAD_CHACHA20-POLY1305 are:
711	   o  A 256-bit key
712	   o  A 96-bit nonce - different for each invocation with the same key.
713	   o  An arbitrary length plaintext
714	   o  Arbitrary length additional authenticated data (AAD)

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

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

725	   o  First, a Poly1305 one-time key is generated from the 256-bit key
726	      and nonce using the procedure described in Section 2.6.
727	   o  Next, the ChaCha20 encryption function is called to encrypt the
728	      plaintext, using the same key and nonce, and with the initial
729	      counter set to 1.
730	   o  Finally, the Poly1305 function is called with the Poly1305 key
731	      calculated above, and a message constructed as a concatenation of
732	      the following:
733	      *  The AAD
734	      *  padding1 - the padding is up to 15 zero bytes, and it brings
735	         the total length so far to an integral multiple of 16.  If the
736	         length of the AAD was already an integral multiple of 16 bytes,
737	         this field is zero-length.
738	      *  The ciphertext
739	      *  padding2 - the padding is up to 15 zero bytes, and it brings
740	         the total length so far to an integral multiple of 16.  If the
741	         length of the ciphertext was already an integral multiple of 16
742	         bytes, this field is zero-length.
743	      *  The length of the additional data in octets (as a 64-bit
744	         little-endian integer).
745	      *  The length of the ciphertext in octets (as a 64-bit little-
746	         endian integer).

748	   Decryption is pretty much the same thing.

750	   The output from the AEAD is twofold:
751	   o  A ciphertext of the same length as the plaintext.
752	   o  A 128-bit tag, which is the output of the Poly1305 function.

754	   A few notes about this design:
755	   1.  The amount of encrypted data possible in a single invocation is
756	       2^32-1 blocks of 64 bytes each, because of the size of the block
757	       counter field in the ChaCha20 block function.  This gives a total
758	       of 247,877,906,880 bytes, or nearly 256 GB.  This should be
759	       enough for traffic protocols such as IPsec and TLS, but may be
760	       too small for file and/or disk encryption.  For such uses, we can
761	       return to the original design, reduce the nonce to 64 bits, and
762	       use the integer at position 13 as the top 32 bits of a 64-bit
763	       block counter, increasing the total message size to over a
764	       million petabytes (1,180,591,620,717,411,303,360 bytes to be
765	       exact).
766	   2.  Despite the previous item, the ciphertext length field in the
767	       construction of the buffer on which Poly1305 runs limits the
768	       ciphertext (and hence, the plaintext) size to 2^64 bytes, or
769	       sixteen thousand petabytes (18,446,744,073,709,551,616 bytes to
770	       be exact).

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

776	2.8.1.  Example and Test Vector for AEAD_CHACHA20-POLY1305

778	   For a test vector, we will use the following inputs to the
779	   AEAD_CHACHA20-POLY1305 function:

781	  Plaintext:
782	  000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
783	  016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
784	  032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
785	  048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
786	  064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
787	  080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
788	  096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
789	  112  74 2e                                            t.

791	   AAD:
792	   000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7              PQRS........

794	  Key:
795	  000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
796	  016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

798	   IV:
799	   000  40 41 42 43 44 45 46 47                          @ABCDEFG

801	   32-bit fixed-common part:
802	   000  07 00 00 00                                      ....

804	   Set up for generating poly1305 one-time key (sender id=7):
805	       61707865  3320646e  79622d32  6b206574
806	       83828180  87868584  8b8a8988  8f8e8d8c
807	       93929190  97969594  9b9a9998  9f9e9d9c
808	       00000000  00000007  43424140  47464544

810	   After generating Poly1305 one-time key:
811	       252bac7b  af47b42d  557ab609  8455e9a4
812	       73d6e10a  ebd97510  7875932a  ff53d53e
813	       decc7ea2  b44ddbad  e49c17d1  d8430bc9
814	       8c94b7bc  8b7d4b4b  3927f67d  1669a432

816	  Poly1305 Key:
817	  000  7b ac 2b 25 2d b4 47 af 09 b6 7a 55 a4 e9 55 84  {.+%-.G...zU..U.
818	  016  0a e1 d6 73 10 75 d9 eb 2a 93 75 78 3e d5 53 ff  ...s.u..*.ux>.S.

820	  Poly1305 r =  455e9a4057ab6080f47b42c052bac7b
821	  Poly1305 s = ff53d53e7875932aebd9751073d6e10a

823	   Keystream bytes:
824	   9f:7b:e9:5d:01:fd:40:ba:15:e2:8f:fb:36:81:0a:ae:
825	   c1:c0:88:3f:09:01:6e:de:dd:8a:d0:87:55:82:03:a5:
826	   4e:9e:cb:38:ac:8e:5e:2b:b8:da:b2:0f:fa:db:52:e8:
827	   75:04:b2:6e:be:69:6d:4f:60:a4:85:cf:11:b8:1b:59:
828	   fc:b1:c4:5f:42:19:ee:ac:ec:6a:de:c3:4e:66:69:78:
829	   8e:db:41:c4:9c:a3:01:e1:27:e0:ac:ab:3b:44:b9:cf:
830	   5c:86:bb:95:e0:6b:0d:f2:90:1a:b6:45:e4:ab:e6:22:
831	   15:38

833	  Ciphertext:
834	  000  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
835	  016  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
836	  032  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
837	  048  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
838	  064  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
839	  080  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
840	  096  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
841	  112  61 16                                            a.

843	  AEAD Construction for Poly1305:
844	  000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 00 00 00 00  PQRS............
845	  016  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
846	  032  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
847	  048  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
848	  064  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
849	  080  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
850	  096  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
851	  112  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
852	  128  61 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00  a...............
853	  144  0c 00 00 00 00 00 00 00 72 00 00 00 00 00 00 00  ........r.......

855	   Note the 4 zero bytes in line 000 and the 14 zero bytes in line 128

857	   Tag:
858	   1a:e1:0b:59:4f:09:e2:6a:7e:90:2e:cb:d0:60:06:91

860	3.  Implementation Advice

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

874	   It is not recommended to use a generic big number library such as the
875	   one in OpenSSL for the arithmetic operations in Poly1305.  Such
876	   libraries use dynamic allocation to be able to handle any-sized
877	   integer, but that flexibility comes at the expense of performance as
878	   well as side-channel security.  More efficient implementations that
879	   run in constant time are available, one of them in DJB's own library,
880	   NaCl ([NaCl]).  A constant-time but not optimal approach would be to
881	   naively implement the arithmetic operations for a 288-bit integers,
882	   because even a naive implementation will not exceed 2^288 in the
883	   multiplication of (acc+block) and r.  An efficient constant-time
884	   implementation can be found in the public domain library poly1305-
885	   donna ([poly1305_donna]).

887	4.  Security Considerations

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

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

896	   Proving the security of either of these is beyond the scope of this
897	   document.  Such proofs are available in the referenced academic
898	   papers.

900	   The most important security consideration in implementing this draft
901	   is the uniqueness of the nonce used in ChaCha20.  Counters and LFSRs
902	   are both acceptable ways of generating unique nonces, as is
903	   encrypting a counter using a 64-bit cipher such as DES.  Note that it
904	   is not acceptable to use a truncation of a counter encrypted with a
905	   128-bit or 256-bit cipher, because such a truncation may repeat after
906	   a short time.

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

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

924	   For Poly1305, the operations are addition, multiplication and
925	   modulus, all on >128-bit numbers.  This can be done in constant time,
926	   but a naive implementation (such as using some generic big number
927	   library) will not be constant time.  For example, if the
928	   multiplication is performed as a separate operation from the modulus,
929	   the result will some times be under 2^256 and some times be above
930	   2^256.  Implementers should be careful about timing side-channels for
931	   Poly1305 by using the appropriate implementation of these operations.

933	5.  IANA Considerations

935	   There are no IANA considerations for this document.

937	6.  Acknowledgements

939	   ChaCha20 and Poly1305 were invented by Daniel J. Bernstein.  The AEAD
940	   construction and the method of creating the one-time poly1305 key
941	   were invented by Adam Langley.

943	   Thanks to Robert Ransom, Watson Ladd, Stefan Buhler, and Kenny
944	   Paterson for their helpful comments and explanations.  Thanks to
945	   Niels Moeller for suggesting the more efficient AEAD construction in
946	   this document.  Special thanks to Ilari Liusvaara for providing extra
947	   test vectors, helpful comments, and for being the first to attempt an
948	   implementation from this draft.

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

953	7.  Changes from Previous Versions

955	   NOTE TO RFC EDITOR: PLEASE REMOVE THIS SECTION BEFORE PUBLICATION

957	7.1.  Changes from version -00 to version -01

959	   Added references to [LatinDances2] and [Procter].

961	   Added this section.

963	7.2.  Changes from draft-nir-cfrg to draft-irtf-cfrg

965	   Added references to [Zhenqing2012] and [LatinDances].

967	   Many clarifications and improved terminology.

969	   More test vectors from Illari.

971	8.  References

973	8.1.  Normative References

975	   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
976	              Requirement Levels", BCP 14, RFC 2119, March 1997.

978	   [chacha]   Bernstein, D., "ChaCha, a variant of Salsa20", Jan 2008.

980	   [poly1305]
981	              Bernstein, D., "The Poly1305-AES message-authentication
982	              code", Mar 2005.

984	8.2.  Informative References

986	   [AE]       Bellare, M. and C. Namprempre, "Authenticated Encryption:
987	              Relations among notions and analysis of the generic
988	              composition paradigm",
989	              <http://cseweb.ucsd.edu/~mihir/papers/oem.html>.

991	   [FIPS-197]
992	              National Institute of Standards and Technology, "Advanced
993	              Encryption Standard (AES)", FIPS PUB 197, November 2001.

995	   [FIPS-46]  National Institute of Standards and Technology, "Data
996	              Encryption Standard", FIPS PUB 46-2, December 1993,
997	              <http://www.itl.nist.gov/fipspubs/fip46-2.htm>.

999	   [LatinDances]
1000	              Aumasson, J., Fischer, S., Khazaei, S., Meier, W., and C.
1001	              Rechberger, "New Features of Latin Dances: Analysis of
1002	              Salsa, ChaCha, and Rumba", Dec 2007.

1004	   [LatinDances2]
1005	              Ishiguro, T., Kiyomoto, S., and Y. Miyake, "Latin Dances
1006	              Revisited: New Analytic Results of Salsa20 and ChaCha",
1007	              Feb 2012.

1009	   [NaCl]     Bernstein, D., Lange, T., and P. Schwabe, "NaCl:
1010	              Networking and Cryptography library",
1011	              <http://nacl.cace-project.eu/index.html>.

1013	   [Procter]  Procter, G., "A Security Analysis of the Composition of
1014	              ChaCha20 and Poly1305", Aug 2014.

1016	   [RFC4868]  Kelly, S. and S. Frankel, "Using HMAC-SHA-256, HMAC-SHA-
1017	              384, and HMAC-SHA-512 with IPsec", RFC 4868, May 2007.

1019	   [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
1020	              Encryption", RFC 5116, January 2008.

1022	   [RFC5996]  Kaufman, C., Hoffman, P., Nir, Y., and P. Eronen,
1023	              "Internet Key Exchange Protocol Version 2 (IKEv2)",
1024	              RFC 5996, September 2010.

1026	   [Zhenqing2012]
1027	              Zhenqing, S., Bin, Z., Dengguo, F., and W. Wenling,
1028	              "Improved key recovery attacks on reduced-round salsa20
1029	              and chacha", 2012.

1031	   [poly1305_donna]
1032	              Floodyberry, A., "Poly1305-donna",
1033	              <https://github.com/floodyberry/poly1305-donna>.

1035	   [standby-cipher]
1036	              McGrew, D., Grieco, A., and Y. Sheffer, "Selection of
1037	              Future Cryptographic Standards",
1038	              draft-mcgrew-standby-cipher (work in progress).

1040	Appendix A.  Additional Test Vectors

1042	   The sub-sections of this appendix contain more test vectors for the
1043	   algorithms in the sub-sections of Section 2.

1045	A.1.  The ChaCha20 Block Functions

1047	  Test Vector #1:
1048	  ==============

1050	  Key:
1051	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1052	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1054	  Nonce:
1055	  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

1057	  Block Counter = 0

1059	    ChaCha State at the end
1060	        ade0b876  903df1a0  e56a5d40  28bd8653
1061	        b819d2bd  1aed8da0  ccef36a8  c70d778b
1062	        7c5941da  8d485751  3fe02477  374ad8b8
1063	        f4b8436a  1ca11815  69b687c3  8665eeb2

1065	  Keystream:
1066	  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
1067	  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
1068	  032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
1069	  048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

1071	  Test Vector #2:
1072	  ==============

1074	  Key:
1075	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1076	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1078	  Nonce:
1079	  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

1081	  Block Counter = 1

1083	    ChaCha State at the end
1084	        bee7079f  7a385155  7c97ba98  0d082d73
1085	        a0290fcb  6965e348  3e53c612  ed7aee32
1086	        7621b729  434ee69c  b03371d5  d539d874
1087	        281fed31  45fb0a51  1f0ae1ac  6f4d794b

1089	  Keystream:
1090	  000  9f 07 e7 be 55 51 38 7a 98 ba 97 7c 73 2d 08 0d  ....UQ8z...|s-..
1091	  016  cb 0f 29 a0 48 e3 65 69 12 c6 53 3e 32 ee 7a ed  ..).H.ei..S>2.z.
1092	  032  29 b7 21 76 9c e6 4e 43 d5 71 33 b0 74 d8 39 d5  ).!v..NC.q3.t.9.
1093	  048  31 ed 1f 28 51 0a fb 45 ac e1 0a 1f 4b 79 4d 6f  1..(Q..E....KyMo

1095	  Test Vector #3:
1096	  ==============

1098	  Key:
1099	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1100	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

1102	  Nonce:
1103	  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

1105	  Block Counter = 1

1107	    ChaCha State at the end
1108	        2452eb3a  9249f8ec  8d829d9b  ddd4ceb1
1109	        e8252083  60818b01  f38422b8  5aaa49c9
1110	        bb00ca8e  da3ba7b4  c4b592d1  fdf2732f
1111	        4436274e  2561b3c8  ebdd4aa6  a0136c00

1113	  Keystream:
1114	  000  3a eb 52 24 ec f8 49 92 9b 9d 82 8d b1 ce d4 dd  :.R$..I.........
1115	  016  83 20 25 e8 01 8b 81 60 b8 22 84 f3 c9 49 aa 5a  . %....`."...I.Z
1116	  032  8e ca 00 bb b4 a7 3b da d1 92 b5 c4 2f 73 f2 fd  ......;...../s..
1117	  048  4e 27 36 44 c8 b3 61 25 a6 4a dd eb 00 6c 13 a0  N'6D..a%.J...l..

1119	  Test Vector #4:
1120	  ==============

1122	  Key:
1123	  000  00 ff 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1124	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1126	  Nonce:
1127	  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

1129	  Block Counter = 2

1131	    ChaCha State at the end
1132	        fb4dd572  4bc42ef1  df922636  327f1394
1133	        a78dea8f  5e269039  a1bebbc1  caf09aae
1134	        a25ab213  48a6b46c  1b9d9bcb  092c5be6
1135	        546ca624  1bec45d5  87f47473  96f0992e

1137	  Keystream:
1138	  000  72 d5 4d fb f1 2e c4 4b 36 26 92 df 94 13 7f 32  r.M....K6&.....2
1139	  016  8f ea 8d a7 39 90 26 5e c1 bb be a1 ae 9a f0 ca  ....9.&^........
1140	  032  13 b2 5a a2 6c b4 a6 48 cb 9b 9d 1b e6 5b 2c 09  ..Z.l..H.....[,.
1141	  048  24 a6 6c 54 d5 45 ec 1b 73 74 f4 87 2e 99 f0 96  $.lT.E..st......

1143	  Test Vector #5:
1144	  ==============

1146	  Key:
1147	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1148	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1150	  Nonce:
1151	  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

1153	  Block Counter = 0

1155	    ChaCha State at the end
1156	        374dc6c2  3736d58c  b904e24a  cd3f93ef
1157	        88228b1a  96a4dfb3  5b76ab72  c727ee54
1158	        0e0e978a  f3145c95  1b748ea8  f786c297
1159	        99c28f5f  628314e8  398a19fa  6ded1b53

1161	  Keystream:
1162	  000  c2 c6 4d 37 8c d5 36 37 4a e2 04 b9 ef 93 3f cd  ..M7..67J.....?.
1163	  016  1a 8b 22 88 b3 df a4 96 72 ab 76 5b 54 ee 27 c7  ..".....r.v[T.'.
1164	  032  8a 97 0e 0e 95 5c 14 f3 a8 8e 74 1b 97 c2 86 f7  .....\....t.....
1165	  048  5f 8f c2 99 e8 14 83 62 fa 19 8a 39 53 1b ed 6d  _......b...9S..m

1167	A.2.  ChaCha20 Encryption

1169	  Test Vector #1:
1170	  ==============

1172	  Key:
1173	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1174	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1176	  Nonce:
1177	  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

1179	  Initial Block Counter = 0

1181	  Plaintext:
1182	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1183	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1184	  032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1185	  048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1187	  Ciphertext:
1188	  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
1189	  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
1190	  032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
1191	  048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

1193	  Test Vector #2:
1194	  ==============

1196	  Key:
1197	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1198	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

1200	  Nonce:
1201	  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

1203	  Initial Block Counter = 1

1205	  Plaintext:
1206	  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
1207	  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
1208	  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
1209	  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
1210	  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
1211	  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
1212	  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
1213	  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
1214	  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
1215	  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
1216	  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
1217	  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
1218	  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
1219	  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
1220	  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
1221	  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
1222	  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
1223	  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
1224	  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
1225	  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
1226	  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
1227	  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
1228	  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
1229	  368  73 73 65 64 20 74 6f                             ssed to

1231	  Ciphertext:
1232	  000  a3 fb f0 7d f3 fa 2f de 4f 37 6c a2 3e 82 73 70  ...}../.O7l.>.sp
1233	  016  41 60 5d 9f 4f 4f 57 bd 8c ff 2c 1d 4b 79 55 ec  A`].OOW...,.KyU.
1234	  032  2a 97 94 8b d3 72 29 15 c8 f3 d3 37 f7 d3 70 05  *....r)....7..p.
1235	  048  0e 9e 96 d6 47 b7 c3 9f 56 e0 31 ca 5e b6 25 0d  ....G...V.1.^.%.
1236	  064  40 42 e0 27 85 ec ec fa 4b 4b b5 e8 ea d0 44 0e  @B.'....KK....D.
1237	  080  20 b6 e8 db 09 d8 81 a7 c6 13 2f 42 0e 52 79 50   ........./B.RyP
1238	  096  42 bd fa 77 73 d8 a9 05 14 47 b3 29 1c e1 41 1c  B..ws....G.)..A.
1239	  112  68 04 65 55 2a a6 c4 05 b7 76 4d 5e 87 be a8 5a  h.eU*....vM^...Z
1240	  128  d0 0f 84 49 ed 8f 72 d0 d6 62 ab 05 26 91 ca 66  ...I..r..b..&..f
1241	  144  42 4b c8 6d 2d f8 0e a4 1f 43 ab f9 37 d3 25 9d  BK.m-....C..7.%.
1242	  160  c4 b2 d0 df b4 8a 6c 91 39 dd d7 f7 69 66 e9 28  ......l.9...if.(
1243	  176  e6 35 55 3b a7 6c 5c 87 9d 7b 35 d4 9e b2 e6 2b  .5U;.l\..{5....+
1244	  192  08 71 cd ac 63 89 39 e2 5e 8a 1e 0e f9 d5 28 0f  .q..c.9.^.....(.
1245	  208  a8 ca 32 8b 35 1c 3c 76 59 89 cb cf 3d aa 8b 6c  ..2.5.<vY...=..l
1246	  224  cc 3a af 9f 39 79 c9 2b 37 20 fc 88 dc 95 ed 84  .:..9y.+7 ......
1247	  240  a1 be 05 9c 64 99 b9 fd a2 36 e7 e8 18 b0 4b 0b  ....d....6....K.
1248	  256  c3 9c 1e 87 6b 19 3b fe 55 69 75 3f 88 12 8c c0  ....k.;.Uiu?....
1249	  272  8a aa 9b 63 d1 a1 6f 80 ef 25 54 d7 18 9c 41 1f  ...c..o..%T...A.
1250	  288  58 69 ca 52 c5 b8 3f a3 6f f2 16 b9 c1 d3 00 62  Xi.R..?.o......b
1251	  304  be bc fd 2d c5 bc e0 91 19 34 fd a7 9a 86 f6 e6  ...-.....4......
1252	  320  98 ce d7 59 c3 ff 9b 64 77 33 8f 3d a4 f9 cd 85  ...Y...dw3.=....
1253	  336  14 ea 99 82 cc af b3 41 b2 38 4d d9 02 f3 d1 ab  .......A.8M.....
1254	  352  7a c6 1d d2 9c 6f 21 ba 5b 86 2f 37 30 e3 7c fd  z....o!.[./70.|.
1255	  368  c4 fd 80 6c 22 f2 21                             ...l".!
1256	  Test Vector #3:
1257	  ==============

1259	  Key:
1260	  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
1261	  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

1263	  Nonce:
1264	  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

1266	  Initial Block Counter = 42

1268	  Plaintext:
1269	  000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
1270	  016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
1271	  032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
1272	  048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
1273	  064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
1274	  080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
1275	  096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
1276	  112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

1278	  Ciphertext:
1279	  000  62 e6 34 7f 95 ed 87 a4 5f fa e7 42 6f 27 a1 df  b.4....._..Bo'..
1280	  016  5f b6 91 10 04 4c 0d 73 11 8e ff a9 5b 01 e5 cf  _....L.s....[...
1281	  032  16 6d 3d f2 d7 21 ca f9 b2 1e 5f b1 4c 61 68 71  .m=..!...._.Lahq
1282	  048  fd 84 c5 4f 9d 65 b2 83 19 6c 7f e4 f6 05 53 eb  ...O.e...l....S.
1283	  064  f3 9c 64 02 c4 22 34 e3 2a 35 6b 3e 76 43 12 a6  ..d.."4.*5k>vC..
1284	  080  1a 55 32 05 57 16 ea d6 96 25 68 f8 7d 3f 3f 77  .U2.W....%h.}??w
1285	  096  04 c6 a8 d1 bc d1 bf 4d 50 d6 15 4b 6d a7 31 b1  .......MP..Km.1.
1286	  112  87 b5 8d fd 72 8a fa 36 75 7a 79 7a c1 88 d1     ....r..6uzyz...

1288	A.3.  Poly1305 Message Authentication Code

1290	   Notice how in test vector #2 r is equal to zero.  The part of the
1291	   Poly1305 algorithm where the accumulator is multiplied by r means
1292	   that with r equal zero, the tag will be equal to s regardless of the
1293	   content of the Text.  Fortunately, all the proposed methods of
1294	   generating r are such that getting this particular weak key is very
1295	   unlikely.

1297	  Test Vector #1:
1298	  ==============

1300	  One-time Poly1305 Key:
1301	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1302	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1304	  Text to MAC:
1305	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1306	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1307	  032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1308	  048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1310	  Tag:
1311	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1313	  Test Vector #2:
1314	  ==============

1316	  One-time Poly1305 Key:
1317	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1318	  016  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

1320	  Text to MAC:
1321	  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
1322	  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
1323	  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
1324	  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
1325	  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
1326	  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
1327	  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
1328	  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
1329	  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
1330	  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
1331	  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
1332	  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
1333	  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
1334	  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
1335	  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
1336	  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
1337	  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
1338	  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
1339	  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
1340	  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
1341	  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
1342	  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
1343	  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
1344	  368  73 73 65 64 20 74 6f                             ssed to

1346	  Tag:
1347	  000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>
1348	  Test Vector #3:
1349	  ==============

1351	  One-time Poly1305 Key:
1352	  000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>
1353	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1355	  Text to MAC:
1356	  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
1357	  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
1358	  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
1359	  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
1360	  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
1361	  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
1362	  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
1363	  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
1364	  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
1365	  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
1366	  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
1367	  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
1368	  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
1369	  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
1370	  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
1371	  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
1372	  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
1373	  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
1374	  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
1375	  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
1376	  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
1377	  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
1378	  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
1379	  368  73 73 65 64 20 74 6f                             ssed to

1381	  Tag:
1382	  000  f3 47 7e 7c d9 54 17 af 89 a6 b8 79 4c 31 0c f0  .G~|.T.....yL1..

1384	  Test Vector #4:
1385	  ==============

1387	  One-time Poly1305 Key:
1388	  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
1389	  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

1391	  Text to MAC:
1392	  000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
1393	  016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
1394	  032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
1395	  048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
1396	  064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
1397	  080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
1398	  096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
1399	  112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

1401	  Tag:
1402	  000  45 41 66 9a 7e aa ee 61 e7 08 dc 7c bc c5 eb 62  EAf.~..a...|...b

1404	   Test Vector #5: If one uses 130-bit partial reduction, does the code
1405	   handle the case where partially reduced final result is not fully
1406	   reduced?

1408	   R:
1409	   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1410	   S:
1411	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1412	   data:
1413	   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1414	   tag:
1415	   03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

1417	   Test Vector #6: What happens if addition of s overflows modulo 2^128?

1419	   R:
1420	   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1421	   S:
1422	   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1423	   data:
1424	   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1425	   tag:
1426	   03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1427	   Test Vector #7: What happens if data limb is all ones and there is
1428	   carry from lower limb?

1430	   R:
1431	   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1432	   S:
1433	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1434	   data:
1435	   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1436	   F0 FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1437	   11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1438	   tag:
1439	   05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

1441	   Test Vector #8: What happens if final result from polynomial part is
1442	   exactly 2^130-5?

1444	   R:
1445	   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1446	   S:
1447	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1448	   data:
1449	   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1450	   FB FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE
1451	   01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
1452	   tag:
1453	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

1455	   Test Vector #9: What happens if final result from polynomial part is
1456	   exactly 2^130-6?

1458	   R:
1459	   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1460	   S:
1461	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1462	   data:
1463	   FD FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1464	   tag:
1465	   FA FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
1466	   Test Vector #10: What happens if 5*H+L-type reduction produces 131-
1467	   bit intermediate result?

1469	   R:
1470	   01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
1471	   S:
1472	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1473	   data:
1474	   E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
1475	   33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
1476	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1477	   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1478	   tag:
1479	   14 00 00 00 00 00 00 00 55 00 00 00 00 00 00 00

1481	   Test Vector #11: What happens if 5*H+L-type reduction produces 131-
1482	   bit final result?

1484	   R:
1485	   01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
1486	   S:
1487	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1488	   data:
1489	   E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
1490	   33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
1491	   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
1492	   tag:
1493	   13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

1495	A.4.  Poly1305 Key Generation Using ChaCha20

1497	  Test Vector #1:
1498	  ==============

1500	  The key:
1501	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1502	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

1504	  The nonce:
1505	  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

1507	  Poly1305 one-time key:
1508	  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
1509	  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..

1511	  Test Vector #2:
1512	  ==============

1514	  The key:
1515	  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
1516	  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

1518	  The nonce:
1519	  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

1521	  Poly1305 one-time key:
1522	  000  ec fa 25 4f 84 5f 64 74 73 d3 cb 14 0d a9 e8 76  ..%O._dts......v
1523	  016  06 cb 33 06 6c 44 7b 87 bc 26 66 dd e3 fb b7 39  ..3.lD{..&f....9

1525	  Test Vector #3:
1526	  ==============

1528	  The key:
1529	  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
1530	  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

1532	  The nonce:
1533	  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

1535	  Poly1305 one-time key:
1536	  000  96 5e 3b c6 f9 ec 7e d9 56 08 08 f4 d2 29 f9 4b  .^;...~.V....).K
1537	  016  13 7f f2 75 ca 9b 3f cb dd 59 de aa d2 33 10 ae  ...u..?..Y...3..

1539	A.5.  ChaCha20-Poly1305 AEAD Decryption

1541	   Below we'll see decrypting a message.  We receive a ciphertext, a
1542	   nonce, and a tag.  We know the key.  We will check the tag, and then
1543	   (assuming that it validates) decrypt the ciphertext.  In this
1544	   particular protocol, we'll assume that there is no padding of the
1545	   plaintext.

1547	  The key:
1548	  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
1549	  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

1551	  Ciphertext:
1552	  000  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
1553	  016  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
1554	  032  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
1555	  048  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
1556	  064  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
1557	  080  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
1558	  096  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
1559	  112  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
1560	  128  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
1561	  144  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
1562	  160  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
1563	  176  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
1564	  192  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
1565	  208  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
1566	  224  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
1567	  240  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
1568	  256  a6 ad 5c b4 02 2b 02 70 9b                       ..\..+.p.

1570	  The nonce:
1571	  000  00 00 00 00 01 02 03 04 05 06 07 08              ............

1573	  The AAD:
1574	  000  f3 33 88 86 00 00 00 00 00 00 4e 91              .3........N.

1576	  Received Tag:
1577	  000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8
1578	   First, we calculate the one-time Poly1305 key

1580	  @@@  ChaCha state with key set up
1581	        61707865  3320646e  79622d32  6b206574
1582	        a540921c  8ad355eb  868833f3  f0b5f604
1583	        c1173947  09802b40  bc5cca9d  c0757020
1584	        00000000  00000000  04030201  08070605

1586	  @@@  ChaCha state after 20 rounds
1587	        a94af0bd  89dee45c  b64bb195  afec8fa1
1588	        508f4726  63f554c0  1ea2c0db  aa721526
1589	        11b1e514  a0bacc0f  828a6015  d7825481
1590	        e8a4a850  d9dcbbd6  4c2de33a  f8ccd912

1592	  @@@ out bytes:
1593	  bd:f0:4a:a9:5c:e4:de:89:95:b1:4b:b6:a1:8f:ec:af:
1594	  26:47:8f:50:c0:54:f5:63:db:c0:a2:1e:26:15:72:aa

1596	  Poly1305 one-time key:
1597	  000  bd f0 4a a9 5c e4 de 89 95 b1 4b b6 a1 8f ec af  ..J.\.....K.....
1598	  016  26 47 8f 50 c0 54 f5 63 db c0 a2 1e 26 15 72 aa  &G.P.T.c....&.r.

1600	   Next, we construct the AEAD buffer

1602	  Poly1305 Input:
1603	  000  f3 33 88 86 00 00 00 00 00 00 4e 91 00 00 00 00  .3........N.....
1604	  016  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
1605	  032  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
1606	  048  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
1607	  064  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
1608	  080  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
1609	  096  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
1610	  112  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
1611	  128  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
1612	  144  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
1613	  160  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
1614	  176  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
1615	  192  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
1616	  208  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
1617	  224  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
1618	  240  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
1619	  256  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
1620	  272  a6 ad 5c b4 02 2b 02 70 9b 00 00 00 00 00 00 00  ..\..+.p........
1621	  288  0c 00 00 00 00 00 00 00 09 01 00 00 00 00 00 00  ................

1623	   We calculate the Poly1305 tag and find that it matches

1625	  Calculated Tag:
1626	  000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

1628	   Finally, we decrypt the ciphertext

1630	  Plaintext::
1631	  000  49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 73 20  Internet-Drafts
1632	  016  61 72 65 20 64 72 61 66 74 20 64 6f 63 75 6d 65  are draft docume
1633	  032  6e 74 73 20 76 61 6c 69 64 20 66 6f 72 20 61 20  nts valid for a
1634	  048  6d 61 78 69 6d 75 6d 20 6f 66 20 73 69 78 20 6d  maximum of six m
1635	  064  6f 6e 74 68 73 20 61 6e 64 20 6d 61 79 20 62 65  onths and may be
1636	  080  20 75 70 64 61 74 65 64 2c 20 72 65 70 6c 61 63   updated, replac
1637	  096  65 64 2c 20 6f 72 20 6f 62 73 6f 6c 65 74 65 64  ed, or obsoleted
1638	  112  20 62 79 20 6f 74 68 65 72 20 64 6f 63 75 6d 65   by other docume
1639	  128  6e 74 73 20 61 74 20 61 6e 79 20 74 69 6d 65 2e  nts at any time.
1640	  144  20 49 74 20 69 73 20 69 6e 61 70 70 72 6f 70 72   It is inappropr
1641	  160  69 61 74 65 20 74 6f 20 75 73 65 20 49 6e 74 65  iate to use Inte
1642	  176  72 6e 65 74 2d 44 72 61 66 74 73 20 61 73 20 72  rnet-Drafts as r
1643	  192  65 66 65 72 65 6e 63 65 20 6d 61 74 65 72 69 61  eference materia
1644	  208  6c 20 6f 72 20 74 6f 20 63 69 74 65 20 74 68 65  l or to cite the
1645	  224  6d 20 6f 74 68 65 72 20 74 68 61 6e 20 61 73 20  m other than as
1646	  240  2f e2 80 9c 77 6f 72 6b 20 69 6e 20 70 72 6f 67  /...work in prog
1647	  256  72 65 73 73 2e 2f e2 80 9d                       ress./...

1649	Authors' Addresses

1651	   Yoav Nir
1652	   Check Point Software Technologies Ltd.
1653	   5 Hasolelim st.
1654	   Tel Aviv  6789735
1655	   Israel

1657	   Email: ynir.ietf@gmail.com

1659	   Adam Langley
1660	   Google Inc

1662	   Email: agl@google.com