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Checking references for intended status: Informational ---------------------------------------------------------------------------- -- Looks like a reference, but probably isn't: '3' on line 474 -- Looks like a reference, but probably isn't: '7' on line 475 -- Looks like a reference, but probably isn't: '11' on line 476 -- Looks like a reference, but probably isn't: '15' on line 477 -- Looks like a reference, but probably isn't: '4' on line 478 -- Looks like a reference, but probably isn't: '8' on line 479 -- Looks like a reference, but probably isn't: '12' on line 480 -- Looks like a reference, but probably isn't: '16' on line 472 Summary: 0 errors (**), 0 flaws (~~), 8 warnings (==), 10 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: August 4, 2014 Google Inc 6 January 31, 2014 8 ChaCha20 and Poly1305 for IETF protocols 9 draft-nir-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 August 4, 2014. 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 . . . . . . . . . . . . . . . . . . 10 65 2.5.1. Poly1305 Example and Test Vector . . . . . . . . . . . 12 66 2.6. Generating the Poly1305 key using ChaCha20 . . . . . . . . 13 67 2.7. AEAD Construction . . . . . . . . . . . . . . . . . . . . 14 68 2.7.1. Example and Test Vector for AEAD_CHACHA20-POLY1305 . . 15 69 3. Implementation Advice . . . . . . . . . . . . . . . . . . . . 17 70 4. Security Considerations . . . . . . . . . . . . . . . . . . . 18 71 5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19 72 6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 19 73 7. References . . . . . . . . . . . . . . . . . . . . . . . . . . 19 74 7.1. Normative References . . . . . . . . . . . . . . . . . . . 19 75 7.2. Informative References . . . . . . . . . . . . . . . . . . 19 76 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 20 78 1. Introduction 80 The Advanced Encryption Standard (AES - [FIPS-197]) has become the 81 gold standard in encryption. Its efficient design, wide 82 implementation, and hardware support allow for high performance in 83 many areas. On most modern platforms, AES is anywhere from 4x to 10x 84 as fast as the previous most-used cipher, 3-key Data Encryption 85 Standard (3DES - [FIPS-46]), which makes it not only the best choice, 86 but the only choice. 88 The problem is that if future advances in cryptanalysis reveal a 89 weakness in AES, users will be in an unenviable position. With the 90 only other widely supported cipher being the much slower 3DES, it is 91 not feasible to re-configure implementations to use 3DES. 92 [standby-cipher] describes this issue and the need for a standby 93 cipher in greater detail. 95 This document defines such a standby cipher. We use ChaCha20 96 ([chacha]) with or without the Poly1305 ([poly1305]) authenticator. 97 These algorithms are not just fast and secure. They are fast even if 98 software-only C-language implementations, allowing for much quicker 99 deployment when compared with algorithms such as AES that are 100 significantly accelerated by hardware implementations. 102 These document does not introduce these new algorithms. They have 103 been defined in scientific papers by D. J. Bernstein, which are 104 referenced by this document. The purpose of this document is to 105 serve as a stable reference for IETF documents making use of these 106 algorithms. 108 1.1. Conventions Used in This Document 110 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 111 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this 112 document are to be interpreted as described in [RFC2119]. 114 The description of the ChaCha algorithm will at various time refer to 115 the ChaCha state as a "vector" or as a "matrix". This follows the 116 use of these terms in DJB's paper. The matrix notation is more 117 visually convenient, and gives a better notion as to why some rounds 118 are called "column rounds" while others are called "diagonal rounds". 119 Here's a diagram of how to martices relate to vectors (using the C 120 language convention of zero being the index origin). 122 0 1 2 3 123 4 5 6 7 124 8 9 10 11 125 12 13 14 15 127 The elements in this vector or matrix are 32-bit unsigned integers. 129 The algorithm name is "ChaCha". "ChaCha20" is a specific instance 130 where 20 "rounds" (or 80 quarter rounds - see Section 2.1) are used. 131 Other variations are defined, with 8 or 12 rounds, but in this 132 document we only describe the 20-round ChaCha, so the names "ChaCha" 133 and "ChaCha20" will be used interchangeably. 135 2. The Algorithms 137 The subsections below describe the algorithms used and the AEAD 138 construction. 140 2.1. The ChaCha Quarter Round 142 The basic operation of the ChaCha algorithm is the quarter round. It 143 operates on four 32-bit unsigned integers, denoted a, b, c, and d. 144 The operation is as follows (in C-like notation): 145 o a += b; d ^= a; d <<<= 16; 146 o c += d; b ^= c; b <<<= 12; 147 o a += b; d ^= a; d <<<= 8; 148 o c += d; b ^= c; b <<<= 7; 149 Where "+" denotes integer addition without carry, "^" denotes a 150 bitwise XOR, and "<<< n" denotes an n-bit left rotation (towards the 151 high bits). 153 For example, let's see the add, XOR and roll operations from the 154 first line with sample numbers: 155 o b = 0x01020304 156 o a = 0x11111111 157 o d = 0x01234567 158 o a = a + b = 0x11111111 + 0x01020304 = 0x12131415 159 o d = d ^ a = 0x01234567 ^ 0x12131415 = 0x13305172 160 o d = d<<<16 = 0x51721330 162 2.1.1. Test Vector for the ChaCha Quarter Round 164 For a test vector, we will use the same numbers as in the example, 165 adding something random for c. 166 o a = 0x11111111 167 o b = 0x01020304 168 o c = 0x9b8d6f43 169 o d = 0x01234567 171 After running a Quarter Round on these 4 numbers, we get these: 173 o a = 0xea2a92f4 174 o b = 0xcb1cf8ce 175 o c = 0x4581472e 176 o d = 0x5881c4bb 178 2.2. A Quarter Round on the ChaCha State 180 The ChaCha state does not have 4 integer numbers, but 16. So the 181 quarter round operation works on only 4 of them - hence the name. 182 Each quarter round operates on 4 pre-determined numbers in the ChaCha 183 state. We will denote by QUATERROUND(x,y,z,w) a quarter-round 184 operation on the numbers at indexes x, y, z, and w of the ChaCha 185 state when viewed as a vector. For example, if we apply 186 QUARTERROUND(1,5,9,13) to a state, this means running the quarter 187 round operation on the elements marked with an asterisk, while 188 leaving the others alone: 190 0 *a 2 3 191 4 *b 6 7 192 8 *c 10 11 193 12 *d 14 15 195 Note that this run of quarter round is part of what is called a 196 "column round". 198 2.2.1. Test Vector for the Quarter Round on the ChaCha state 200 For a test vector, we will use a ChaCha state that was generated 201 randomly: 203 Sample ChaCha State 205 879531e0 c5ecf37d 516461b1 c9a62f8a 206 44c20ef3 3390af7f d9fc690b 2a5f714c 207 53372767 b00a5631 974c541a 359e9963 208 5c971061 3d631689 2098d9d6 91dbd320 210 We will apply the QUARTERROUND(2,7,8,13) operation to this state. 211 For obvious reasons, this one is part of what is called a "diagonal 212 round": 214 After applying QUARTERROUND(2,7,8,13) 216 879531e0 c5ecf37d bdb886dc c9a62f8a 217 44c20ef3 3390af7f d9fc690b cfacafd2 218 e46bea80 b00a5631 974c541a 359e9963 219 5c971061 ccc07c79 2098d9d6 91dbd320 221 Note that only the numbers in positions 2, 7, 8, and 13 changed. 223 2.3. The ChaCha20 block Function 225 The ChaCha block function transforms a ChaCha state by running 226 multiple quarter rounds. 228 The inputs to ChaCha20 are: 229 o A 256-bit key, treated as a concatenation of 8 32-bit little- 230 endian integers. 231 o A 96-bit nonce, treated as a concatenation of 3 32-bit little- 232 endian integers. 233 o A 32-bit block count parameter, treated as a 32-bit little-endian 234 integer. 236 The output is 64 random-looking bytes. 238 The ChaCha algorithm described here uses a 256-bit key. The original 239 algorithm also specified 128-bit keys and 8- and 12-round variants, 240 but these are out of scope for this document. In this section we 241 describe the ChaCha block function. 243 Note also that the original ChaCha had a 64-bit nonce and 64-bit 244 block count. We have modified this here to be more consistent with 245 recommendations in section 3.2 of [RFC5116]. This limits the use of 246 a single (key,nonce) combination to 2^32 blocks, or 256 GB, but that 247 is enough for most uses. In cases where a single key is used by 248 multiple senders, it is important to make sure that they don't use 249 the same nonces. This can be assured by partitioning the nonce space 250 so that the first 32 bits are unique per sender, while the other 64 251 bits come from a counter. 253 The ChaCha20 as follows: 254 o The first 4 words (0-3) are constants: 0x61707865, 0x3320646e, 255 0x79622d32, 0x6b206574. 256 o The next 8 words (4-11) are taken from the 256-bit key by reading 257 the bytes in little-endian order, in 4-byte chunks. 258 o Word 12 is a block counter. Since each block is 64-byte, a 32-bit 259 word is enough for 256 Gigabytes of data. 261 o Words 13-15 are a nonce, which should not be repeated for the same 262 key. The 13th word is the first 32 bits of the input nonce taken 263 as a little-endian integer, while the 15th word is the last 32 264 bits. 266 cccccccc cccccccc cccccccc cccccccc 267 kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk 268 kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk 269 bbbbbbbb nnnnnnnn nnnnnnnn nnnnnnnn 271 c=constant k=key b=blockcount n=nonce 273 ChaCha20 runs 20 rounds, alternating between "column" and "diagonal" 274 rounds. Each round is 4 quarter-rounds, and they are run as follows. 275 Rounds 1-4 are part of the "column" round, while 5-8 are part of the 276 "diagonal" round: 277 1. QUARTERROUND ( 0, 4, 8,12) 278 2. QUARTERROUND ( 1, 5, 9,13) 279 3. QUARTERROUND ( 2, 6,10,14) 280 4. QUARTERROUND ( 3, 7,11,15) 281 5. QUARTERROUND ( 0, 5,10,15) 282 6. QUARTERROUND ( 1, 6,11,12) 283 7. QUARTERROUND ( 2, 7, 8,13) 284 8. QUARTERROUND ( 3, 4, 9,14) 286 At the end of 20 rounds, the original input words are added to the 287 output words, and the result is serialized by sequencing the words 288 one-by-one in little-endian order. 290 2.3.1. Test Vector for the ChaCha20 Block Function 292 For a test vector, we will use the following inputs to the ChaCha20 293 block function: 294 o Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13: 295 14:15:16:17:18:19:1a:1b:1c:1d:1e:1f. The key is a sequence of 296 octets with no particular structure before we copy it into the 297 ChaCha state. 298 o Nonce = (00:00:00:09:00:00:00:4a:00:00:00:00) 299 o Block Count = 1. 301 After setting up the ChaCha state, it looks like this: 303 ChaCha State with the key set up. 305 61707865 3320646e 79622d32 6b206574 306 03020100 07060504 0b0a0908 0f0e0d0c 307 13121110 17161514 1b1a1918 1f1e1d1c 308 00000001 09000000 4a000000 00000000 310 After running 20 rounds (10 column rounds interleaved with 10 311 diagonal rounds), the ChaCha state looks like this: 313 ChaCha State after 20 rounds 315 837778ab e238d763 a67ae21e 5950bb2f 316 c4f2d0c7 fc62bb2f 8fa018fc 3f5ec7b7 317 335271c2 f29489f3 eabda8fc 82e46ebd 318 d19c12b4 b04e16de 9e83d0cb 4e3c50a2 320 Finally we add the original state to the result (simple vector or 321 matrix addition), giving this: 323 ChaCha State at the end of the ChaCha20 operation 325 e4e7f110 15593bd1 1fdd0f50 c47120a3 326 c7f4d1c7 0368c033 9aaa2204 4e6cd4c3 327 466482d2 09aa9f07 05d7c214 a2028bd9 328 d19c12b5 b94e16de e883d0cb 4e3c50a2 330 2.4. The ChaCha20 encryption algorithm 332 ChaCha20 is a stream cipher designed by D. J. Bernstein. It is a 333 refinement of the Salsa20 algorithm, and uses a 256-bit key. 335 ChaCha20 successively calls the ChaCha20 block function, with the 336 same key and nonce, and with successively increasing block counter 337 parameters. The resulting state is then serialized by writing the 338 numbers in little-endian order. Concatenating the results from the 339 successive blocks forms a key stream, which is then XOR-ed with the 340 plaintext. There is no requirement for the plaintext to be an 341 integral multiple of 512-bits. If there is extra keystream from the 342 last block, it is discarded. Specific protocols MAY require that the 343 plaintext and ciphertext have certain length. Such protocols need to 344 specify how the plaintext is padded, and how much padding it 345 receives. 347 The inputs to ChaCha20 are: 348 o A 256-bit key 349 o A 32-bit initial counter. This can be set to any number, but will 350 usually be zero or one. It makes sense to use 1 if we use the 351 zero block for something else, such as generating a one-time 352 authenticator key as part of an AEAD algorithm. 353 o A 96-bit nonce. In some protocols, this is known as the 354 Initialization Vector. 355 o an arbitrary-length plaintext 357 The output is an encrypted message of the same length. 359 2.4.1. Example and Test Vector for the ChaCha20 Cipher 361 For a test vector, we will use the following inputs to the ChaCha20 362 block function: 363 o Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13: 364 14:15:16:17:18:19:1a:1b:1c:1d:1e:1f. 365 o Nonce = (00:00:00:00:00:00:00:4a:00:00:00:00). 366 o Initial Counter = 1. 368 We use the following for the plaintext. It was chosen to be long 369 enough to require more than one block, but not so long that it would 370 make this example cumbersome (so, less than 3 blocks): 372 Plaintext Sunscreen: 373 000 4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c|Ladies and Gentl 374 016 65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73|emen of the clas 375 032 73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63|s of '99: If I c 376 048 6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f|ould offer you o 377 064 6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20|nly one tip for 378 080 74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73|the future, suns 379 096 63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69|creen would be i 380 112 74 2e |t. 382 The following figure shows 4 ChaCha state matrices: 383 1. First block as it is set up. 384 2. Second block as it is set up. Note that these blocks are only 385 two bits apart - only the counter in position 12 is different. 386 3. Third block is the first block after the ChaCha20 block 387 operation. 388 4. Final block is the second block after the ChaCha20 block 389 operation was applied. 390 After that, we show the keystream. 392 First block setup: 393 61707865 3320646e 79622d32 6b206574 394 03020100 07060504 0b0a0908 0f0e0d0c 395 13121110 17161514 1b1a1918 1f1e1d1c 396 00000001 00000000 4a000000 00000000 398 Second block setup: 399 61707865 3320646e 79622d32 6b206574 400 03020100 07060504 0b0a0908 0f0e0d0c 401 13121110 17161514 1b1a1918 1f1e1d1c 402 00000002 00000000 4a000000 00000000 404 First block after block operation: 405 f3514f22 e1d91b40 6f27de2f ed1d63b8 406 821f138c e2062c3d ecca4f7e 78cff39e 407 a30a3b8a 920a6072 cd7479b5 34932bed 408 40ba4c79 cd343ec6 4c2c21ea b7417df0 410 Second block after block operation: 411 9f74a669 410f633f 28feca22 7ec44dec 412 6d34d426 738cb970 3ac5e9f3 45590cc4 413 da6e8b39 892c831a cdea67c1 2b7e1d90 414 037463f3 a11a2073 e8bcfb88 edc49139 416 Keystream: 417 22:4f:51:f3:40:1b:d9:e1:2f:de:27:6f:b8:63:1d:ed:8c:13:1f:82:3d:2c:06 418 e2:7e:4f:ca:ec:9e:f3:cf:78:8a:3b:0a:a3:72:60:0a:92:b5:79:74:cd:ed:2b 419 93:34:79:4c:ba:40:c6:3e:34:cd:ea:21:2c:4c:f0:7d:41:b7:69:a6:74:9f:3f 420 63:0f:41:22:ca:fe:28:ec:4d:c4:7e:26:d4:34:6d:70:b9:8c:73:f3:e9:c5:3a 421 c4:0c:59:45:39:8b:6e:da:1a:83:2c:89:c1:67:ea:cd:90:1d:7e:2b:f3:63 423 Finally, we XOR the Keystream with the plaintext, yielding the 424 Ciphertext: 426 Ciphertext Sunscreen: 427 000 6e 2e 35 9a 25 68 f9 80 41 ba 07 28 dd 0d 69 81|n.5.%h..A..(..i. 428 016 e9 7e 7a ec 1d 43 60 c2 0a 27 af cc fd 9f ae 0b|.~z..C`..'...... 429 032 f9 1b 65 c5 52 47 33 ab 8f 59 3d ab cd 62 b3 57|..e.RG3..Y=..b.W 430 048 16 39 d6 24 e6 51 52 ab 8f 53 0c 35 9f 08 61 d8|.9.$.QR..S.5..a. 431 064 07 ca 0d bf 50 0d 6a 61 56 a3 8e 08 8a 22 b6 5e|....P.jaV....".^ 432 080 52 bc 51 4d 16 cc f8 06 81 8c e9 1a b7 79 37 36|R.QM.........y76 433 096 5a f9 0b bf 74 a3 5b e6 b4 0b 8e ed f2 78 5e 42|Z...t.[......x^B 434 112 87 4d |.M 436 2.5. The Poly1305 algorithm 438 Poly1305 is a one-time authenticator designed by D. J. Bernstein. 439 Poly1305 takes a 32-byte one-time key and a message and produces a 440 16-byte tag. 442 The original article ([poly1305]) is entitled "The Poly1305-AES 443 message-authentication code", and the MAC function there requires a 444 128-bit AES key, a 128-bit "additional key", and a 128-bit (non- 445 secret) nonce. AES is used there for encrypting the nonce, so as to 446 get a unique (and secret) 128-bit string, but as the paper states, 447 "There is nothing special about AES here. One can replace AES with 448 an arbitrary keyed function from an arbitrary set of nonces to 16- 449 byte strings.". 451 Regardless of how the key is generated, the key is partitioned into 452 two parts, called "r" and "s". The pair (r,s) should be unique, and 453 MUST be unpredictable for each invocation (that is why it was 454 originally obtained by encrypting a nonce), while "r" MAY be 455 constant, but needs to be modified as follows before being used: ("r" 456 is treated as a 16-octet little-endian number): 457 o r[3], r[7], r[11], and r[15] are required to have their top four 458 bits clear (be smaller than 16) 459 o r[4], r[8], and r[12] are required to have their bottom two bits 460 clear (be divisible by 4) 462 The following sample code clamps "r" to be appropriate: 464 /* 465 Adapted from poly1305aes_test_clamp.c version 20050207 466 D. J. Bernstein 467 Public domain. 468 */ 470 #include "poly1305aes_test.h" 472 void poly1305aes_test_clamp(unsigned char r[16]) 473 { 474 r[3] &= 15; 475 r[7] &= 15; 476 r[11] &= 15; 477 r[15] &= 15; 478 r[4] &= 252; 479 r[8] &= 252; 480 r[12] &= 252; 481 } 483 The "s" should be unpredictable, but it is perfectly acceptable to 484 generate both "r" and "s" uniquely each time. Because each of them 485 is 128-bit, pseudo-randomly generating them (see Section 2.6) is also 486 acceptable. 488 The inputs to Poly1305 are: 489 o A 256-bit one-time key 490 o An arbitrary length message 492 The output is a 128-bit tag. 494 First, the "r" value should be clamped. 496 Next, set the constant prime "P" be 2^130-5: 497 3fffffffffffffffffffffffffffffffb. Also set a variable "accumulator" 498 to zero. 500 Next, divide the message into 16-byte blocks. The last one might be 501 shorter: 502 o Read the block as a little-endian number. 503 o Add one bit beyond the number of octets. For a 16-byte block this 504 is equivalent to adding 2^128 to the number. For the shorter 505 block it can be 2^120, 2^112, or any power of two that is evenly 506 divisible by 8, all the way down to 2^8. 507 o If the block is not 17 bytes long (the last block), pad it with 508 zeros. This is meaningless if you're treating it them as numbers. 509 o Add this number to the accumulator. 510 o Multiply by "r" 511 o Set the accumulator to the result modulo p. To summarize: Acc = 512 ((Acc+block)*r) % p. 514 Finally, the value of the secret key "s" is added to the accumulator, 515 and the 128 least significant bits are serialized in little-endian 516 order to form the tag. 518 2.5.1. Poly1305 Example and Test Vector 520 For our example, we will dispense with generating the one-time key 521 using AES, and assume that we got the following keying material: 522 o Key Material: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8:01: 523 03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b 524 o s as an octet string: 01:03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49: 525 f5:1b 526 o s as a 128-bit number: 1bf54941aff6bf4afdb20dfb8a800301 527 o r before clamping: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8 528 o Clamped r as a number: 806d5400e52447c036d555408bed685. 530 For our message, we'll use a short text: 532 Message to be Authenticated: 533 000 43 72 79 70 74 6f 67 72 61 70 68 69 63 20 46 6f|Cryptographic Fo 534 016 72 75 6d 20 52 65 73 65 61 72 63 68 20 47 72 6f|rum Research Gro 535 032 75 70 |up 537 Since Poly1305 works in 16-byte chunks, the 34-byte message divides 538 into 3 blocks. In the following calculation, "Acc" denotes the 539 accumulator and "Block" the current block: 541 Block #1 543 Acc = 00 544 Block = 6f4620636968706172676f7470797243 545 Block with 0x01 byte = 016f4620636968706172676f7470797243 546 Acc + block = 016f4620636968706172676f7470797243 547 (Acc+Block) * r = 548 b83fe991ca66800489155dcd69e8426ba2779453994ac90ed284034da565ecf 549 Acc = ((Acc+Block)*r) % P = 2c88c77849d64ae9147ddeb88e69c83fc 551 Block #2 553 Acc = 2c88c77849d64ae9147ddeb88e69c83fc 554 Block = 6f7247206863726165736552206d7572 555 Block with 0x01 byte = 016f7247206863726165736552206d7572 556 Acc + block = 437febea505c820f2ad5150db0709f96e 557 (Acc+Block) * r = 558 21dcc992d0c659ba4036f65bb7f88562ae59b32c2b3b8f7efc8b00f78e548a26 559 Acc = ((Acc+Block)*r) % P = 2d8adaf23b0337fa7cccfb4ea344b30de 561 Last Block 563 Acc = 2d8adaf23b0337fa7cccfb4ea344b30de 564 Block = 7075 565 Block with 0x01 byte = 017075 566 Acc + block = 2d8adaf23b0337fa7cccfb4ea344ca153 567 (Acc + Block) * r = 568 16d8e08a0f3fe1de4fe4a15486aca7a270a29f1e6c849221e4a6798b8e45321f 569 ((Acc + Block) * r) % P = 28d31b7caff946c77c8844335369d03a7 571 Adding s we get this number, and serialize if to get the tag: 573 Acc + s = 2a927010caf8b2bc2c6365130c11d06a8 575 Tag: a8:06:1d:c1:30:51:36:c6:c2:2b:8b:af:0c:01:27:a9 577 2.6. Generating the Poly1305 key using ChaCha20 579 As said in Section 2.5, it is acceptable to generate the one-time 580 Poly1305 pseudo-randomly. This section proposes such a method. 582 To generate such a key pair (r,s), we will use the ChaCha20 block 583 function described in Section 2.3. This assumes that we have a 256- 584 bit session key for the MAC function, such as SK_ai and SK_ar in 585 IKEv2, the integrity key in ESP and AH, or the client_write_MAC_key 586 and server_write_MAC_key in TLS. Any document that specifies the use 587 of Poly1305 as a MAC algorithm for some protocol must specify that 588 256 bits are allocated for the integrity key. 590 The method is to call the block function with the following 591 parameters: 592 o The 256-bit session integrity key is used as the ChaCha20 key. 593 o The block counter is set to zero. 594 o The protocol will specify a 96-bit or 64-bit nonce. This MUST be 595 unique per invocation with the same key, so it MUST NOT be 596 randomly generated. A counter is a good way to implement this, 597 but other methods, such as an LFSR are also acceptable. ChaCha20 598 as specified here requires a 96-bit nonce. So if the provided 599 nonce is only 64-bit, then the first 32 bits of the nonce will be 600 set to a constant number. This will usually be zero, but for 601 protocols with multiple sender, it may be different for each 602 sender, but should be the same for all invocations of the function 603 with the same key by a particular sender. 605 After running the block function, we have a 512-bit state. We take 606 the first 256 bits or the serialized state, and use those as the one- 607 time Poly1305 key: The first 128 bits are clamped, and form "r", 608 while the next 128 bits become "s". The other 256 bits are 609 discarded. 611 Note that while many protocols have provisions for a nonce for 612 encryption algorithms (often called Initialization Vectors, or IVs), 613 they usually don't have such a provision for the MAC function. In 614 that case the per-invocation nonce will have to come from somewhere 615 else, such as a message counter. 617 2.7. AEAD Construction 619 Note: Much of the content of this document, including this AEAD 620 construction is taken from Adam Langley's draft ([agl-draft]) for the 621 use of these algorithms in TLS. The AEAD construction described here 622 is called AEAD_CHACHA20-POLY1305. 624 AEAD_CHACHA20-POLY1305 is an authenticated encryption with additional 625 data algorithm. The inputs to AEAD_CHACHA20-POLY1305 are: 626 o A 256-bit key 627 o A 96-bit nonce - different for each invocation with the same key. 628 o An arbitrary length plaintext 629 o Arbitrary length additional data 631 The ChaCha20 and Poly1305 primitives are combined into an AEAD that 632 takes a 256-bit key and 64-bit IV as follows: 633 o First the 96-bit nonce is constructed by prepending a 32-bit 634 constant value to the IV. This could be set to zero, or could be 635 derived from keying material, or could be assigned to a sender. 636 It is up to the specific protocol to define the source for that 637 32-bit value. 639 o Next, a Poly1305 one-time key is generated from the 256-bit key 640 and nonce using the procedure described in Section 2.6. 641 o The ChaCha20 encryption function is called to encrypt the 642 plaintext, using the same key and nonce, and with the initial 643 counter set to 1. 644 o The Poly1305 function is called with the Poly1305 key calculated 645 above, and a message constructed as a concatenation of the 646 following: 647 * The additional data 648 * The length of the additional data in octets (as a 64-bit 649 little-endian integer). TBD: bit count rather than octets? 650 network order? 651 * The ciphertext 652 * The length of the ciphertext in octets (as a 64-bit little- 653 endian integer). TBD: bit count rather than octets? network 654 order? 656 Decryption is pretty much the same thing. 658 The output from the AEAD is twofold: 659 o A ciphertext of the same length as the plaintext. 660 o A 128-bit tag, which is the output of the Poly1305 function. 662 A few notes about this design: 663 1. The amount of encrypted data possible in a single invocation is 664 2^32-1 blocks of 64 bytes each, for a total of 247,877,906,880 665 bytes, or nearly 256 GB. This should be enough for traffic 666 protocols such as IPsec and TLS, but may be too small for file 667 and/or disk encryption. For such uses, we can return to the 668 original design, reduce the nonce to 64 bits, and use the integer 669 at position 13 as the top 32 bits of a 64-bit block counter, 670 increasing the total message size to over a million petabytes 671 (1,180,591,620,717,411,303,360 bytes to be exact). 672 2. Despite the previous item, the ciphertext length field in the 673 construction of the buffer on which Poly1305 runs limits the 674 ciphertext (and hence, the plaintext) size to 2^64 bytes, or 675 sixteen thousand petabytes (18,446,744,073,709,551,616 bytes to 676 be exact). 678 2.7.1. Example and Test Vector for AEAD_CHACHA20-POLY1305 680 For a test vector, we will use the following inputs to the 681 AEAD_CHACHA20-POLY1305 function: 683 Plaintext: 684 000 4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c|Ladies and Gentl 685 016 65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73|emen of the clas 686 032 73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63|s of '99: If I c 687 048 6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f|ould offer you o 688 064 6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20|nly one tip for 689 080 74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73|the future, suns 690 096 63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69|creen would be i 691 112 74 2e |t. 693 AAD: 694 000 50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 PQRS........ 696 Key: 697 000 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f|................ 698 016 90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f|................ 700 IV: 701 000 40 41 42 43 44 45 46 47 @ABCDEFG 703 32-bit fixed-common part: 704 000 07 00 00 00 .... 706 Set up for generating poly1305 one-time key (sender id=7): 707 61707865 3320646e 79622d32 6b206574 708 83828180 87868584 8b8a8988 8f8e8d8c 709 93929190 97969594 9b9a9998 9f9e9d9c 710 00000000 00000007 43424140 47464544 712 After generating Poly1305 one-time key: 713 252bac7b af47b42d 557ab609 8455e9a4 714 73d6e10a ebd97510 7875932a ff53d53e 715 decc7ea2 b44ddbad e49c17d1 d8430bc9 716 8c94b7bc 8b7d4b4b 3927f67d 1669a432 718 Poly1305 Key: 719 000 7b ac 2b 25 2d b4 47 af 09 b6 7a 55 a4 e9 55 84|{.+%-.G...zU..U. 720 016 0a e1 d6 73 10 75 d9 eb 2a 93 75 78 3e d5 53 ff|...s.u..*.ux>.S. 722 Poly1305 r = 455e9a4057ab6080f47b42c052bac7b 723 Poly1305 s = ff53d53e7875932aebd9751073d6e10a 724 Keystream bytes: 725 9f:7b:e9:5d:01:fd:40:ba:15:e2:8f:fb:36:81:0a:ae: 726 c1:c0:88:3f:09:01:6e:de:dd:8a:d0:87:55:82:03:a5: 727 4e:9e:cb:38:ac:8e:5e:2b:b8:da:b2:0f:fa:db:52:e8: 728 75:04:b2:6e:be:69:6d:4f:60:a4:85:cf:11:b8:1b:59: 729 fc:b1:c4:5f:42:19:ee:ac:ec:6a:de:c3:4e:66:69:78: 730 8e:db:41:c4:9c:a3:01:e1:27:e0:ac:ab:3b:44:b9:cf: 731 5c:86:bb:95:e0:6b:0d:f2:90:1a:b6:45:e4:ab:e6:22: 732 15:38 734 Ciphertext: 735 000 d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2|...4d.`.{...S.~. 736 016 a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6|...Q)n......6.b. 737 032 3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b|=..^..g....i..r. 738 048 1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36|.q.....)....~.;6 739 064 92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58|...-w......(..X 740 080 fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc|..$...u.U...H1.. 741 096 3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b|?....Kz..v.e...K 742 112 61 16 |a. 744 AEAD Construction for Poly1305: 745 000 50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 0c 00 00 00|PQRS............ 746 016 00 00 00 00 d3 1a 8d 34 64 8e 60 db 7b 86 af bc|.......4d.`.{... 747 032 53 ef 7e c2 a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7|S.~....Q)n...... 748 048 36 ee 62 d6 3d be a4 5e 8c a9 67 12 82 fa fb 69|6.b.=..^..g....i 749 064 da 92 72 8b 1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6|..r..q.....).... 750 080 7e cd 3b 36 92 dd bd 7f 2d 77 8b 8c 98 03 ae e3|~.;6...-w...... 751 096 28 09 1b 58 fa b3 24 e4 fa d6 75 94 55 85 80 8b|(..X..$...u.U... 752 112 48 31 d7 bc 3f f4 de f0 8e 4b 7a 9d e5 76 d2 65|H1..?....Kz..v.e 753 128 86 ce c6 4b 61 16 72 00 00 00 00 00 00 00 |...Ka.r....... 755 Tag: 756 18:fb:11:a5:03:1a:d1:3a:7e:3b:03:d4:6e:e3:a6:a7 758 3. Implementation Advice 760 Each block of ChaCha20 involves 16 move operations and one increment 761 operation for loading the state, 80 each of XOR, addition and Roll 762 operations for the rounds, 16 more add operations and 16 XOR 763 operations for protecting the plaintext. Section 2.3 describes the 764 ChaCha block function as "adding the original input words". This 765 implies that before starting the rounds on the ChaCha state, it is 766 copied aside only to be added in later. This would be correct, but 767 it saves a few operations to instead copy the state and do the work 768 on the copy. This way, for the next block you don't need to recreate 769 the state, but only to increment the block counter. This saves 770 approximately 5.5% of the cycles. 772 It is NOT RECOMMENDED to use a generic big number library such as the 773 one in OpenSSL for the arithmetic operations in Poly1305. Such 774 libraries use dynamic allocation to be able to handle any-sized 775 integer, but that flexibility comes at the expense of performance as 776 well as side-channel security. More efficient implementations that 777 run in constant time are available, one of them in DJB's own library, 778 NaCl ([NaCl]). 780 4. Security Considerations 782 The ChaCha20 cipher is designed to provide 256-bit security. 784 The Poly1305 authenticator is designed to ensure that forged messages 785 are rejected with a probability of 1-(n/(2^102)) for a 16n-byte 786 message, even after sending 2^64 legitimate messages, so it is SUF- 787 CMA in the terminology of [AE]. 789 Proving the security of either of these is beyond the scope of this 790 document. Such proofs are available in the referenced academic 791 papers. 793 The most important security consideration in implementing this draft 794 is the uniqueness of the nonce used in ChaCha20. Counters and LFSRs 795 are both acceptable ways of generating unique nonces, as is 796 encrypting a counter using a 64-bit cipher such as DES. Note that it 797 is not acceptable to use a truncation of a counter encrypted with a 798 128-bit or 256-bit cipher, because such a truncation may repeat after 799 a short time. 801 The Poly1305 key MUST be unpredictable to an attacker. Randomly 802 generating the key would fulfill this requirement, except that 803 Poly1305 is often used in communications protocols, so the receiver 804 should know the key. Pseudo-random number generation such as by 805 encrypting a counter is acceptable. Using ChaCha with a secret key 806 and a nonce is also acceptable. 808 The algorithms presented here were designed to be easy to implement 809 in constant time to avoid side-channel vulnerabilities. The 810 operations used in ChaCha20 are all additions, XORs, and fixed 811 rotations. All of these can and should be implemented in constant 812 time. Access to offsets into the ChaCha state and the number of 813 operations do not depend on any property of the key, eliminating the 814 chance of information about the key leaking through the timing of 815 cache misses. 817 For Poly1305, the operations are addition, multiplication and 818 modulus, all on >128-bit numbers. This can be done in constant time, 819 but a naive implementation (such as using some generic big number 820 library) will not be constant time. For example, if the 821 multiplication is performed as a separate operation from the modulus, 822 the result will some times be under 2^256 and some times be above 823 2^256. Implementers should be careful about timing side-channels for 824 Poly1305 by using the appropriate implementation of these operations. 826 5. IANA Considerations 828 There are no IANA considerations for this document. 830 6. Acknowledgements 832 None of the algorithms here are my own. ChaCha20 and Poly1305 were 833 invented by Daniel J. Bernstein, and the AEAD construction was 834 invented by Adam Langley. 836 Thanks to Robert Ransom and Ilari Liusvaara for their helpful 837 comments and explanations. 839 7. References 841 7.1. Normative References 843 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 844 Requirement Levels", BCP 14, RFC 2119, March 1997. 846 [chacha] Bernstein, D., "ChaCha, a variant of Salsa20", Jan 2008. 848 [poly1305] 849 Bernstein, D., "The Poly1305-AES message-authentication 850 code", Mar 2005. 852 7.2. Informative References 854 [AE] Bellare, M. and C. Namprempre, "Authenticated Encryption: 855 Relations among notions and analysis of the generic 856 composition paradigm", 857 . 859 [FIPS-197] 860 National Institute of Standards and Technology, "Advanced 861 Encryption Standard (AES)", FIPS PUB 197, November 2001. 863 [FIPS-46] National Institute of Standards and Technology, "Data 864 Encryption Standard", FIPS PUB 46-2, December 1993, 865 . 867 [NaCl] Bernstein, D., Lange, T., and P. Schwabe, "NaCl: 868 Networking and Cryptography library", 869 . 871 [RFC5116] McGrew, D., "An Interface and Algorithms for Authenticated 872 Encryption", RFC 5116, January 2008. 874 [agl-draft] 875 Langley, A. and W. Chang, "ChaCha20 and Poly1305 based 876 Cipher Suites for TLS", draft-agl-tls-chacha20poly1305-04 877 (work in progress), November 2013. 879 [standby-cipher] 880 McGrew, D., Grieco, A., and Y. Sheffer, "Selection of 881 Future Cryptographic Standards", 882 draft-mcgrew-standby-cipher (work in progress). 884 Authors' Addresses 886 Yoav Nir 887 Check Point Software Technologies Ltd. 888 5 Hasolelim st. 889 Tel Aviv 6789735 890 Israel 892 Email: synp71@live.com 894 Adam Langley 895 Google Inc 897 Email: agl@google.com