RFC 7539
ChaCha20 and Poly1305 for IETF Protocols
Internet Research Task Force (IRTF) Y. Nir Request for Comments: 7539 Check Point Category: Informational A. Langley ISSN: 2070-1721 Google, Inc. May 2015 ChaCha20 and Poly1305 for IETF ProtocolsAbstract
This document defines the ChaCha20 stream cipher as well as the use of the Poly1305 authenticator, both as stand-alone algorithms and as a "combined mode", or Authenticated Encryption with Associated Data (AEAD) algorithm. This document does not introduce any new crypto, but is meant to serve as a stable reference and an implementation guide. It is a product of the Crypto Forum Research Group (CFRG). Status of This Memo This document is not an Internet Standards Track specification; it is published for informational purposes. This document is a product of the Internet Research Task Force (IRTF). The IRTF publishes the results of Internet-related research and development activities. These results might not be suitable for deployment. This RFC represents the consensus of the Crypto Forum Research Group of the Internet Research Task Force (IRTF). Documents approved for publication by the IRSG are not a candidate for any level of Internet Standard; see Section 2 of RFC 5741. Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfc-editor.org/info/rfc7539. Copyright Notice Copyright (c) 2015 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document.
Table of Contents
1. Introduction ....................................................3 1.1. Conventions Used in This Document ..........................4 2. The Algorithms ..................................................4 2.1. The ChaCha Quarter Round ...................................4 2.1.1. Test Vector for the ChaCha Quarter Round ............5 2.2. A Quarter Round on the ChaCha State ........................5 2.2.1. Test Vector for the Quarter Round on the ChaCha State ........................................6 2.3. The ChaCha20 Block Function ................................6 2.3.1. The ChaCha20 Block Function in Pseudocode ...........8 2.3.2. Test Vector for the ChaCha20 Block Function .........9 2.4. The ChaCha20 Encryption Algorithm .........................10 2.4.1. The ChaCha20 Encryption Algorithm in Pseudocode ....11 2.4.2. Example and Test Vector for the ChaCha20 Cipher ....11 2.5. The Poly1305 Algorithm ....................................13 2.5.1. The Poly1305 Algorithms in Pseudocode ..............15 2.5.2. Poly1305 Example and Test Vector ...................15 2.6. Generating the Poly1305 Key Using ChaCha20 ................17 2.6.1. Poly1305 Key Generation in Pseudocode ..............18 2.6.2. Poly1305 Key Generation Test Vector ................18 2.7. A Pseudorandom Function for Crypto Suites based on ChaCha/Poly1305 ...........................................18 2.8. AEAD Construction .........................................19 2.8.1. Pseudocode for the AEAD Construction ...............21 2.8.2. Example and Test Vector for AEAD_CHACHA20_POLY1305 .............................22 3. Implementation Advice ..........................................24 4. Security Considerations ........................................24 5. IANA Considerations ............................................26 6. References .....................................................26 6.1. Normative References ......................................26 6.2. Informative References ....................................26 Appendix A. Additional Test Vectors ...............................29 A.1. The ChaCha20 Block Functions ...............................29 A.2. ChaCha20 Encryption ........................................32 A.3. Poly1305 Message Authentication Code .......................34 A.4. Poly1305 Key Generation Using ChaCha20 .....................40 A.5. ChaCha20-Poly1305 AEAD Decryption ..........................41 Appendix B. Performance Measurements of ChaCha20 ..................44 Acknowledgements ..................................................45 Authors' Addresses ................................................45
1. Introduction
The Advanced Encryption Standard (AES -- [FIPS-197]) has become the gold standard in encryption. Its efficient design, widespread implementation, and hardware support allow for high performance in many areas. On most modern platforms, AES is anywhere from four to ten times as fast as the previous most-used cipher, Triple Data Encryption Standard (3DES -- [SP800-67]), which makes it not only the best choice, but the only practical choice. There are several problems with this. If future advances in cryptanalysis reveal a weakness in AES, users will be in an unenviable position. With the only other widely supported cipher being the much slower 3DES, it is not feasible to reconfigure deployments to use 3DES. [Standby-Cipher] describes this issue and the need for a standby cipher in greater detail. Another problem is that while AES is very fast on dedicated hardware, its performance on platforms that lack such hardware is considerably lower. Yet another problem is that many AES implementations are vulnerable to cache- collision timing attacks ([Cache-Collisions]). This document provides a definition and implementation guide for three algorithms: 1. The ChaCha20 cipher. This is a high-speed cipher first described in [ChaCha]. It is considerably faster than AES in software-only implementations, making it around three times as fast on platforms that lack specialized AES hardware. See Appendix B for some hard numbers. ChaCha20 is also not sensitive to timing attacks (see the security considerations in Section 4). This algorithm is described in Section 2.4 2. The Poly1305 authenticator. This is a high-speed message authentication code. Implementation is also straightforward and easy to get right. The algorithm is described in Section 2.5. 3. The CHACHA20-POLY1305 Authenticated Encryption with Associated Data (AEAD) construction, described in Section 2.8. This document does not introduce these new algorithms for the first time. They have been defined in scientific papers by D. J. Bernstein, which are referenced by this document. The purpose of this document is to serve as a stable reference for IETF documents making use of these algorithms. These algorithms have undergone rigorous analysis. Several papers discuss the security of Salsa and ChaCha ([LatinDances], [LatinDances2], [Zhenqing2012]).
This document represents the consensus of the Crypto Forum Research Group (CFRG).1.1. Conventions Used in This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119]. The description of the ChaCha algorithm will at various time refer to the ChaCha state as a "vector" or as a "matrix". This follows the use of these terms in Professor Bernstein's paper. The matrix notation is more visually convenient and gives a better notion as to why some rounds are called "column rounds" while others are called "diagonal rounds". Here's a diagram of how the matrices relate to vectors (using the C language convention of zero being the index origin). 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 The elements in this vector or matrix are 32-bit unsigned integers. The algorithm name is "ChaCha". "ChaCha20" is a specific instance where 20 "rounds" (or 80 quarter rounds -- see Section 2.1) are used. Other variations are defined, with 8 or 12 rounds, but in this document we only describe the 20-round ChaCha, so the names "ChaCha" and "ChaCha20" will be used interchangeably.2. The Algorithms
The subsections below describe the algorithms used and the AEAD construction.2.1. The ChaCha Quarter Round
The basic operation of the ChaCha algorithm is the quarter round. It operates on four 32-bit unsigned integers, denoted a, b, c, and d. The operation is as follows (in C-like notation): 1. a += b; d ^= a; d <<<= 16; 2. c += d; b ^= c; b <<<= 12; 3. a += b; d ^= a; d <<<= 8; 4. c += d; b ^= c; b <<<= 7;
Where "+" denotes integer addition modulo 2^32, "^" denotes a bitwise Exclusive OR (XOR), and "<<< n" denotes an n-bit left rotation (towards the high bits). For example, let's see the add, XOR, and roll operations from the fourth line with sample numbers: o a = 0x11111111 o b = 0x01020304 o c = 0x77777777 o d = 0x01234567 o c = c + d = 0x77777777 + 0x01234567 = 0x789abcde o b = b ^ c = 0x01020304 ^ 0x789abcde = 0x7998bfda o b = b <<< 7 = 0x7998bfda <<< 7 = 0xcc5fed3c2.1.1. Test Vector for the ChaCha Quarter Round
For a test vector, we will use the same numbers as in the example, adding something random for c. o a = 0x11111111 o b = 0x01020304 o c = 0x9b8d6f43 o d = 0x01234567 After running a Quarter Round on these four numbers, we get these: o a = 0xea2a92f4 o b = 0xcb1cf8ce o c = 0x4581472e o d = 0x5881c4bb2.2. A Quarter Round on the ChaCha State
The ChaCha state does not have four integer numbers: it has 16. So the quarter-round operation works on only four of them -- hence the name. Each quarter round operates on four predetermined numbers in the ChaCha state. We will denote by QUARTERROUND(x,y,z,w) a quarter- round operation on the numbers at indices x, y, z, and w of the ChaCha state when viewed as a vector. For example, if we apply QUARTERROUND(1,5,9,13) to a state, this means running the quarter- round operation on the elements marked with an asterisk, while leaving the others alone: 0 *a 2 3 4 *b 6 7 8 *c 10 11 12 *d 14 15
Note that this run of quarter round is part of what is called a "column round".2.2.1. Test Vector for the Quarter Round on the ChaCha State
For a test vector, we will use a ChaCha state that was generated randomly: Sample ChaCha State 879531e0 c5ecf37d 516461b1 c9a62f8a 44c20ef3 3390af7f d9fc690b 2a5f714c 53372767 b00a5631 974c541a 359e9963 5c971061 3d631689 2098d9d6 91dbd320 We will apply the QUARTERROUND(2,7,8,13) operation to this state. For obvious reasons, this one is part of what is called a "diagonal round": After applying QUARTERROUND(2,7,8,13) 879531e0 c5ecf37d *bdb886dc c9a62f8a 44c20ef3 3390af7f d9fc690b *cfacafd2 *e46bea80 b00a5631 974c541a 359e9963 5c971061 *ccc07c79 2098d9d6 91dbd320 Note that only the numbers in positions 2, 7, 8, and 13 changed.2.3. The ChaCha20 Block Function
The ChaCha block function transforms a ChaCha state by running multiple quarter rounds. The inputs to ChaCha20 are: o A 256-bit key, treated as a concatenation of eight 32-bit little- endian integers. o A 96-bit nonce, treated as a concatenation of three 32-bit little- endian integers. o A 32-bit block count parameter, treated as a 32-bit little-endian integer. The output is 64 random-looking bytes.
The ChaCha algorithm described here uses a 256-bit key. The original algorithm also specified 128-bit keys and 8- and 12-round variants, but these are out of scope for this document. In this section, we describe the ChaCha block function. Note also that the original ChaCha had a 64-bit nonce and 64-bit block count. We have modified this here to be more consistent with recommendations in Section 3.2 of [RFC5116]. This limits the use of a single (key,nonce) combination to 2^32 blocks, or 256 GB, but that is enough for most uses. In cases where a single key is used by multiple senders, it is important to make sure that they don't use the same nonces. This can be assured by partitioning the nonce space so that the first 32 bits are unique per sender, while the other 64 bits come from a counter. The ChaCha20 state is initialized as follows: o The first four words (0-3) are constants: 0x61707865, 0x3320646e, 0x79622d32, 0x6b206574. o The next eight words (4-11) are taken from the 256-bit key by reading the bytes in little-endian order, in 4-byte chunks. o Word 12 is a block counter. Since each block is 64-byte, a 32-bit word is enough for 256 gigabytes of data. o Words 13-15 are a nonce, which should not be repeated for the same key. The 13th word is the first 32 bits of the input nonce taken as a little-endian integer, while the 15th word is the last 32 bits. cccccccc cccccccc cccccccc cccccccc kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk kkkkkkkk bbbbbbbb nnnnnnnn nnnnnnnn nnnnnnnn c=constant k=key b=blockcount n=nonce ChaCha20 runs 20 rounds, alternating between "column rounds" and "diagonal rounds". Each round consists of four quarter-rounds, and they are run as follows. Quarter rounds 1-4 are part of a "column" round, while 5-8 are part of a "diagonal" round: 1. QUARTERROUND ( 0, 4, 8,12) 2. QUARTERROUND ( 1, 5, 9,13) 3. QUARTERROUND ( 2, 6,10,14) 4. QUARTERROUND ( 3, 7,11,15) 5. QUARTERROUND ( 0, 5,10,15)
6. QUARTERROUND ( 1, 6,11,12) 7. QUARTERROUND ( 2, 7, 8,13) 8. QUARTERROUND ( 3, 4, 9,14) At the end of 20 rounds (or 10 iterations of the above list), we add the original input words to the output words, and serialize the result by sequencing the words one-by-one in little-endian order. Note: "addition" in the above paragraph is done modulo 2^32. In some machine languages, this is called carryless addition on a 32-bit word.2.3.1. The ChaCha20 Block Function in Pseudocode
Note: This section and a few others contain pseudocode for the algorithm explained in a previous section. Every effort was made for the pseudocode to accurately reflect the algorithm as described in the preceding section. If a conflict is still present, the textual explanation and the test vectors are normative. inner_block (state): Qround(state, 0, 4, 8,12) Qround(state, 1, 5, 9,13) Qround(state, 2, 6,10,14) Qround(state, 3, 7,11,15) Qround(state, 0, 5,10,15) Qround(state, 1, 6,11,12) Qround(state, 2, 7, 8,13) Qround(state, 3, 4, 9,14) end chacha20_block(key, counter, nonce): state = constants | key | counter | nonce working_state = state for i=1 upto 10 inner_block(working_state) end state += working_state return serialize(state) end
2.3.2. Test Vector for the ChaCha20 Block Function
For a test vector, we will use the following inputs to the ChaCha20 block function: o Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13: 14:15:16:17:18:19:1a:1b:1c:1d:1e:1f. The key is a sequence of octets with no particular structure before we copy it into the ChaCha state. o Nonce = (00:00:00:09:00:00:00:4a:00:00:00:00) o Block Count = 1. After setting up the ChaCha state, it looks like this: ChaCha state with the key setup. 61707865 3320646e 79622d32 6b206574 03020100 07060504 0b0a0908 0f0e0d0c 13121110 17161514 1b1a1918 1f1e1d1c 00000001 09000000 4a000000 00000000 After running 20 rounds (10 column rounds interleaved with 10 "diagonal rounds"), the ChaCha state looks like this: ChaCha state after 20 rounds 837778ab e238d763 a67ae21e 5950bb2f c4f2d0c7 fc62bb2f 8fa018fc 3f5ec7b7 335271c2 f29489f3 eabda8fc 82e46ebd d19c12b4 b04e16de 9e83d0cb 4e3c50a2 Finally, we add the original state to the result (simple vector or matrix addition), giving this: ChaCha state at the end of the ChaCha20 operation e4e7f110 15593bd1 1fdd0f50 c47120a3 c7f4d1c7 0368c033 9aaa2204 4e6cd4c3 466482d2 09aa9f07 05d7c214 a2028bd9 d19c12b5 b94e16de e883d0cb 4e3c50a2
After we serialize the state, we get this: Serialized Block: 000 10 f1 e7 e4 d1 3b 59 15 50 0f dd 1f a3 20 71 c4 .....;Y.P.... q. 016 c7 d1 f4 c7 33 c0 68 03 04 22 aa 9a c3 d4 6c 4e ....3.h.."....lN 032 d2 82 64 46 07 9f aa 09 14 c2 d7 05 d9 8b 02 a2 ..dF............ 048 b5 12 9c d1 de 16 4e b9 cb d0 83 e8 a2 50 3c 4e ......N......P<N2.4. The ChaCha20 Encryption Algorithm
ChaCha20 is a stream cipher designed by D. J. Bernstein. It is a refinement of the Salsa20 algorithm, and it uses a 256-bit key. ChaCha20 successively calls the ChaCha20 block function, with the same key and nonce, and with successively increasing block counter parameters. ChaCha20 then serializes the resulting state by writing the numbers in little-endian order, creating a keystream block. Concatenating the keystream blocks from the successive blocks forms a keystream. The ChaCha20 function then performs an XOR of this keystream with the plaintext. Alternatively, each keystream block can be XORed with a plaintext block before proceeding to create the next block, saving some memory. There is no requirement for the plaintext to be an integral multiple of 512 bits. If there is extra keystream from the last block, it is discarded. Specific protocols MAY require that the plaintext and ciphertext have certain length. Such protocols need to specify how the plaintext is padded and how much padding it receives. The inputs to ChaCha20 are: o A 256-bit key o A 32-bit initial counter. This can be set to any number, but will usually be zero or one. It makes sense to use one if we use the zero block for something else, such as generating a one-time authenticator key as part of an AEAD algorithm. o A 96-bit nonce. In some protocols, this is known as the Initialization Vector. o An arbitrary-length plaintext The output is an encrypted message, or "ciphertext", of the same length.
Decryption is done in the same way. The ChaCha20 block function is used to expand the key into a keystream, which is XORed with the ciphertext giving back the plaintext.2.4.1. The ChaCha20 Encryption Algorithm in Pseudocode
chacha20_encrypt(key, counter, nonce, plaintext): for j = 0 upto floor(len(plaintext)/64)-1 key_stream = chacha20_block(key, counter+j, nonce) block = plaintext[(j*64)..(j*64+63)] encrypted_message += block ^ key_stream end if ((len(plaintext) % 64) != 0) j = floor(len(plaintext)/64) key_stream = chacha20_block(key, counter+j, nonce) block = plaintext[(j*64)..len(plaintext)-1] encrypted_message += (block^key_stream)[0..len(plaintext)%64] end return encrypted_message end2.4.2. Example and Test Vector for the ChaCha20 Cipher
For a test vector, we will use the following inputs to the ChaCha20 block function: o Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13: 14:15:16:17:18:19:1a:1b:1c:1d:1e:1f. o Nonce = (00:00:00:00:00:00:00:4a:00:00:00:00). o Initial Counter = 1. We use the following for the plaintext. It was chosen to be long enough to require more than one block, but not so long that it would make this example cumbersome (so, less than 3 blocks): Plaintext Sunscreen: 000 4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c Ladies and Gentl 016 65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73 emen of the clas 032 73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63 s of '99: If I c 048 6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f ould offer you o 064 6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20 nly one tip for 080 74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73 the future, suns 096 63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69 creen would be i 112 74 2e t.
The following figure shows four ChaCha state matrices:
1. First block as it is set up.
2. Second block as it is set up. Note that these blocks are only
two bits apart -- only the counter in position 12 is different.
3. Third block is the first block after the ChaCha20 block
operation.
4. Final block is the second block after the ChaCha20 block
operation was applied.
After that, we show the keystream.
First block setup:
61707865 3320646e 79622d32 6b206574
03020100 07060504 0b0a0908 0f0e0d0c
13121110 17161514 1b1a1918 1f1e1d1c
00000001 00000000 4a000000 00000000
Second block setup:
61707865 3320646e 79622d32 6b206574
03020100 07060504 0b0a0908 0f0e0d0c
13121110 17161514 1b1a1918 1f1e1d1c
00000002 00000000 4a000000 00000000
First block after block operation:
f3514f22 e1d91b40 6f27de2f ed1d63b8
821f138c e2062c3d ecca4f7e 78cff39e
a30a3b8a 920a6072 cd7479b5 34932bed
40ba4c79 cd343ec6 4c2c21ea b7417df0
Second block after block operation:
9f74a669 410f633f 28feca22 7ec44dec
6d34d426 738cb970 3ac5e9f3 45590cc4
da6e8b39 892c831a cdea67c1 2b7e1d90
037463f3 a11a2073 e8bcfb88 edc49139
Keystream:
22:4f:51:f3:40:1b:d9:e1:2f:de:27:6f:b8:63:1d:ed:8c:13:1f:82:3d:2c:06
e2:7e:4f:ca:ec:9e:f3:cf:78:8a:3b:0a:a3:72:60:0a:92:b5:79:74:cd:ed:2b
93:34:79:4c:ba:40:c6:3e:34:cd:ea:21:2c:4c:f0:7d:41:b7:69:a6:74:9f:3f
63:0f:41:22:ca:fe:28:ec:4d:c4:7e:26:d4:34:6d:70:b9:8c:73:f3:e9:c5:3a
c4:0c:59:45:39:8b:6e:da:1a:83:2c:89:c1:67:ea:cd:90:1d:7e:2b:f3:63
Finally, we XOR the keystream with the plaintext, yielding the ciphertext: Ciphertext Sunscreen: 000 6e 2e 35 9a 25 68 f9 80 41 ba 07 28 dd 0d 69 81 n.5.%h..A..(..i. 016 e9 7e 7a ec 1d 43 60 c2 0a 27 af cc fd 9f ae 0b .~z..C`..'...... 032 f9 1b 65 c5 52 47 33 ab 8f 59 3d ab cd 62 b3 57 ..e.RG3..Y=..b.W 048 16 39 d6 24 e6 51 52 ab 8f 53 0c 35 9f 08 61 d8 .9.$.QR..S.5..a. 064 07 ca 0d bf 50 0d 6a 61 56 a3 8e 08 8a 22 b6 5e ....P.jaV....".^ 080 52 bc 51 4d 16 cc f8 06 81 8c e9 1a b7 79 37 36 R.QM.........y76 096 5a f9 0b bf 74 a3 5b e6 b4 0b 8e ed f2 78 5e 42 Z...t.[......x^B 112 87 4d .M2.5. The Poly1305 Algorithm
Poly1305 is a one-time authenticator designed by D. J. Bernstein. Poly1305 takes a 32-byte one-time key and a message and produces a 16-byte tag. This tag is used to authenticate the message. The original article ([Poly1305]) is titled "The Poly1305-AES message-authentication code", and the MAC function there requires a 128-bit AES key, a 128-bit "additional key", and a 128-bit (non- secret) nonce. AES is used there for encrypting the nonce, so as to get a unique (and secret) 128-bit string, but as the paper states, "There is nothing special about AES here. One can replace AES with an arbitrary keyed function from an arbitrary set of nonces to 16-byte strings." Regardless of how the key is generated, the key is partitioned into two parts, called "r" and "s". The pair (r,s) should be unique, and MUST be unpredictable for each invocation (that is why it was originally obtained by encrypting a nonce), while "r" MAY be constant, but needs to be modified as follows before being used: ("r" is treated as a 16-octet little-endian number): o r[3], r[7], r[11], and r[15] are required to have their top four bits clear (be smaller than 16) o r[4], r[8], and r[12] are required to have their bottom two bits clear (be divisible by 4)
The following sample code clamps "r" to be appropriate:
/*
Adapted from poly1305aes_test_clamp.c version 20050207
D. J. Bernstein
Public domain.
*/
#include "poly1305aes_test.h"
void poly1305aes_test_clamp(unsigned char r[16])
{
r[3] &= 15;
r[7] &= 15;
r[11] &= 15;
r[15] &= 15;
r[4] &= 252;
r[8] &= 252;
r[12] &= 252;
}
The "s" should be unpredictable, but it is perfectly acceptable to
generate both "r" and "s" uniquely each time. Because each of them
is 128 bits, pseudorandomly generating them (see Section 2.6) is also
acceptable.
The inputs to Poly1305 are:
o A 256-bit one-time key
o An arbitrary length message
The output is a 128-bit tag.
First, the "r" value should be clamped.
Next, set the constant prime "P" be 2^130-5:
3fffffffffffffffffffffffffffffffb. Also set a variable "accumulator"
to zero.
Next, divide the message into 16-byte blocks. The last one might be
shorter:
o Read the block as a little-endian number.
o Add one bit beyond the number of octets. For a 16-byte block,
this is equivalent to adding 2^128 to the number. For the shorter
block, it can be 2^120, 2^112, or any power of two that is evenly
divisible by 8, all the way down to 2^8.
o If the block is not 17 bytes long (the last block), pad it with
zeros. This is meaningless if you are treating the blocks as
numbers.
o Add this number to the accumulator.
o Multiply by "r".
o Set the accumulator to the result modulo p. To summarize: Acc =
((Acc+block)*r) % p.
Finally, the value of the secret key "s" is added to the accumulator,
and the 128 least significant bits are serialized in little-endian
order to form the tag.
2.5.1. The Poly1305 Algorithms in Pseudocode
clamp(r): r &= 0x0ffffffc0ffffffc0ffffffc0fffffff
poly1305_mac(msg, key):
r = (le_bytes_to_num(key[0..15])
clamp(r)
s = le_num(key[16..31])
accumulator = 0
p = (1<<130)-5
for i=1 upto ceil(msg length in bytes / 16)
n = le_bytes_to_num(msg[((i-1)*16)..(i*16)] | [0x01])
a += n
a = (r * a) % p
end
a += s
return num_to_16_le_bytes(a)
end
2.5.2. Poly1305 Example and Test Vector
For our example, we will dispense with generating the one-time key
using AES, and assume that we got the following keying material:
o Key Material: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8:01:0
3:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b
o s as an octet string:
01:03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b
o s as a 128-bit number: 1bf54941aff6bf4afdb20dfb8a800301
o r before clamping: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8
o Clamped r as a number: 806d5400e52447c036d555408bed685
For our message, we'll use a short text:
Message to be Authenticated:
000 43 72 79 70 74 6f 67 72 61 70 68 69 63 20 46 6f Cryptographic Fo
016 72 75 6d 20 52 65 73 65 61 72 63 68 20 47 72 6f rum Research Gro
032 75 70 up
Since Poly1305 works in 16-byte chunks, the 34-byte message divides
into three blocks. In the following calculation, "Acc" denotes the
accumulator and "Block" the current block:
Block #1
Acc = 00
Block = 6f4620636968706172676f7470797243
Block with 0x01 byte = 016f4620636968706172676f7470797243
Acc + block = 016f4620636968706172676f7470797243
(Acc+Block) * r =
b83fe991ca66800489155dcd69e8426ba2779453994ac90ed284034da565ecf
Acc = ((Acc+Block)*r) % P = 2c88c77849d64ae9147ddeb88e69c83fc
Block #2
Acc = 2c88c77849d64ae9147ddeb88e69c83fc
Block = 6f7247206863726165736552206d7572
Block with 0x01 byte = 016f7247206863726165736552206d7572
Acc + block = 437febea505c820f2ad5150db0709f96e
(Acc+Block) * r =
21dcc992d0c659ba4036f65bb7f88562ae59b32c2b3b8f7efc8b00f78e548a26
Acc = ((Acc+Block)*r) % P = 2d8adaf23b0337fa7cccfb4ea344b30de
Last Block
Acc = 2d8adaf23b0337fa7cccfb4ea344b30de
Block = 7075
Block with 0x01 byte = 017075
Acc + block = 2d8adaf23b0337fa7cccfb4ea344ca153
(Acc + Block) * r =
16d8e08a0f3fe1de4fe4a15486aca7a270a29f1e6c849221e4a6798b8e45321f
((Acc + Block) * r) % P = 28d31b7caff946c77c8844335369d03a7
Adding s, we get this number, and serialize if to get the tag: Acc + s = 2a927010caf8b2bc2c6365130c11d06a8 Tag: a8:06:1d:c1:30:51:36:c6:c2:2b:8b:af:0c:01:27:a92.6. Generating the Poly1305 Key Using ChaCha20
As said in Section 2.5, it is acceptable to generate the one-time Poly1305 pseudorandomly. This section defines such a method. To generate such a key pair (r,s), we will use the ChaCha20 block function described in Section 2.3. This assumes that we have a 256-bit session key for the Message Authentication Code (MAC) function, such as SK_ai and SK_ar in Internet Key Exchange Protocol version 2 (IKEv2) ([RFC7296]), the integrity key in the Encapsulating Security Payload (ESP) and Authentication Header (AH), or the client_write_MAC_key and server_write_MAC_key in TLS. Any document that specifies the use of Poly1305 as a MAC algorithm for some protocol must specify that 256 bits are allocated for the integrity key. Note that in the AEAD construction defined in Section 2.8, the same key is used for encryption and key generation, so the use of SK_a* or *_write_MAC_key is only for stand-alone Poly1305. The method is to call the block function with the following parameters: o The 256-bit session integrity key is used as the ChaCha20 key. o The block counter is set to zero. o The protocol will specify a 96-bit or 64-bit nonce. This MUST be unique per invocation with the same key, so it MUST NOT be randomly generated. A counter is a good way to implement this, but other methods, such as a Linear Feedback Shift Register (LFSR) are also acceptable. ChaCha20 as specified here requires a 96-bit nonce. So if the provided nonce is only 64-bit, then the first 32 bits of the nonce will be set to a constant number. This will usually be zero, but for protocols with multiple senders it may be different for each sender, but should be the same for all invocations of the function with the same key by a particular sender. After running the block function, we have a 512-bit state. We take the first 256 bits or the serialized state, and use those as the one- time Poly1305 key: the first 128 bits are clamped and form "r", while the next 128 bits become "s". The other 256 bits are discarded.
Note that while many protocols have provisions for a nonce for encryption algorithms (often called Initialization Vectors, or IVs), they usually don't have such a provision for the MAC function. In that case, the per-invocation nonce will have to come from somewhere else, such as a message counter.2.6.1. Poly1305 Key Generation in Pseudocode
poly1305_key_gen(key,nonce): counter = 0 block = chacha20_block(key,counter,nonce) return block[0..31] end2.6.2. Poly1305 Key Generation Test Vector
For this example, we'll set: Key: 000 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f ................ 016 90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f ................ Nonce: 000 00 00 00 00 00 01 02 03 04 05 06 07 ............ The ChaCha state setup with key, nonce, and block counter zero: 61707865 3320646e 79622d32 6b206574 83828180 87868584 8b8a8988 8f8e8d8c 93929190 97969594 9b9a9998 9f9e9d9c 00000000 00000000 03020100 07060504 The ChaCha state after 20 rounds: 8ba0d58a cc815f90 27405081 7194b24a 37b633a8 a50dfde3 e2b8db08 46a6d1fd 7da03782 9183a233 148ad271 b46773d1 3cc1875a 8607def1 ca5c3086 7085eb87 Output bytes: 000 8a d5 a0 8b 90 5f 81 cc 81 50 40 27 4a b2 94 71 ....._...P@'J..q 016 a8 33 b6 37 e3 fd 0d a5 08 db b8 e2 fd d1 a6 46 .3.7...........F And that output is also the 32-byte one-time key used for Poly1305.2.7. A Pseudorandom Function for Crypto Suites based on ChaCha/Poly1305
Some protocols, such as IKEv2 ([RFC7296]), require a Pseudorandom Function (PRF), mostly for key derivation. In the IKEv2 definition, a PRF is a function that accepts a variable-length key and a
variable-length input, and returns a fixed-length output. Most commonly, Hashed MAC (HMAC) constructions are used for this purpose, and often the same function is used for both message authentication and PRF. Poly1305 is not a suitable choice for a PRF. Poly1305 prohibits using the same key twice, whereas the PRF in IKEv2 is used multiple times with the same key. Additionally, unlike HMAC, Poly1305 is biased, so using it for key derivation would reduce the security of the symmetric encryption. Chacha20 could be used as a key-derivation function, by generating an arbitrarily long keystream. However, that is not what protocols such as IKEv2 require. For this reason, this document does not specify a PRF and recommends that crypto suites use some other PRF such as PRF_HMAC_SHA2_256 (see Section 2.1.2 of [RFC4868]).2.8. AEAD Construction
AEAD_CHACHA20_POLY1305 is an authenticated encryption with additional data algorithm. The inputs to AEAD_CHACHA20_POLY1305 are: o A 256-bit key o A 96-bit nonce -- different for each invocation with the same key o An arbitrary length plaintext o Arbitrary length additional authenticated data (AAD) Some protocols may have unique per-invocation inputs that are not 96 bits in length. For example, IPsec may specify a 64-bit nonce. In such a case, it is up to the protocol document to define how to transform the protocol nonce into a 96-bit nonce, for example, by concatenating a constant value. The ChaCha20 and Poly1305 primitives are combined into an AEAD that takes a 256-bit key and 96-bit nonce as follows: o First, a Poly1305 one-time key is generated from the 256-bit key and nonce using the procedure described in Section 2.6. o Next, the ChaCha20 encryption function is called to encrypt the plaintext, using the same key and nonce, and with the initial counter set to 1.
o Finally, the Poly1305 function is called with the Poly1305 key
calculated above, and a message constructed as a concatenation of
the following:
* The AAD
* padding1 -- the padding is up to 15 zero bytes, and it brings
the total length so far to an integral multiple of 16. If the
length of the AAD was already an integral multiple of 16 bytes,
this field is zero-length.
* The ciphertext
* padding2 -- the padding is up to 15 zero bytes, and it brings
the total length so far to an integral multiple of 16. If the
length of the ciphertext was already an integral multiple of 16
bytes, this field is zero-length.
* The length of the additional data in octets (as a 64-bit
little-endian integer).
* The length of the ciphertext in octets (as a 64-bit little-
endian integer).
The output from the AEAD is twofold:
o A ciphertext of the same length as the plaintext.
o A 128-bit tag, which is the output of the Poly1305 function.
Decryption is similar with the following differences:
o The roles of ciphertext and plaintext are reversed, so the
ChaCha20 encryption function is applied to the ciphertext,
producing the plaintext.
o The Poly1305 function is still run on the AAD and the ciphertext,
not the plaintext.
o The calculated tag is bitwise compared to the received tag. The
message is authenticated if and only if the tags match.
A few notes about this design:
1. The amount of encrypted data possible in a single invocation is
2^32-1 blocks of 64 bytes each, because of the size of the block
counter field in the ChaCha20 block function. This gives a total
of 247,877,906,880 bytes, or nearly 256 GB. This should be
enough for traffic protocols such as IPsec and TLS, but may be
too small for file and/or disk encryption. For such uses, we can
return to the original design, reduce the nonce to 64 bits, and
use the integer at position 13 as the top 32 bits of a 64-bit
block counter, increasing the total message size to over a
million petabytes (1,180,591,620,717,411,303,360 bytes to be
exact).
2. Despite the previous item, the ciphertext length field in the
construction of the buffer on which Poly1305 runs limits the
ciphertext (and hence, the plaintext) size to 2^64 bytes, or
sixteen thousand petabytes (18,446,744,073,709,551,616 bytes to
be exact).
The AEAD construction in this section is a novel composition of
ChaCha20 and Poly1305. A security analysis of this composition is
given in [Procter].
Here is a list of the parameters for this construction as defined in
Section 4 of RFC 5116:
o K_LEN (key length) is 32 octets.
o P_MAX (maximum size of the plaintext) is 247,877,906,880 bytes, or
nearly 256 GB.
o A_MAX (maximum size of the associated data) is set to 2^64-1
octets by the length field for associated data.
o N_MIN = N_MAX = 12 octets.
o C_MAX = P_MAX + tag length = 247,877,906,896 octets.
Distinct AAD inputs (as described in Section 3.3 of RFC 5116) shall
be concatenated into a single input to AEAD_CHACHA20_POLY1305. It is
up to the application to create a structure in the AAD input if it is
needed.
2.8.1. Pseudocode for the AEAD Construction
pad16(x):
if (len(x) % 16)==0
then return NULL
else return copies(0, 16-(len(x)%16))
end
chacha20_aead_encrypt(aad, key, iv, constant, plaintext):
nonce = constant | iv
otk = poly1305_key_gen(key, nonce)
ciphertext = chacha20_encrypt(key, 1, nonce, plaintext)
mac_data = aad | pad16(aad)
mac_data |= ciphertext | pad16(ciphertext)
mac_data |= num_to_4_le_bytes(aad.length)
mac_data |= num_to_4_le_bytes(ciphertext.length)
tag = poly1305_mac(mac_data, otk)
return (ciphertext, tag)
2.8.2. Example and Test Vector for AEAD_CHACHA20_POLY1305
For a test vector, we will use the following inputs to the
AEAD_CHACHA20_POLY1305 function:
Plaintext:
000 4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c Ladies and Gentl
016 65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73 emen of the clas
032 73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63 s of '99: If I c
048 6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f ould offer you o
064 6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20 nly one tip for
080 74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73 the future, suns
096 63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69 creen would be i
112 74 2e t.
AAD:
000 50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 PQRS........
Key:
000 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f ................
016 90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f ................
IV:
000 40 41 42 43 44 45 46 47 @ABCDEFG
32-bit fixed-common part:
000 07 00 00 00 ....
Setup for generating Poly1305 one-time key (sender id=7):
61707865 3320646e 79622d32 6b206574
83828180 87868584 8b8a8988 8f8e8d8c
93929190 97969594 9b9a9998 9f9e9d9c
00000000 00000007 43424140 47464544
After generating Poly1305 one-time key:
252bac7b af47b42d 557ab609 8455e9a4
73d6e10a ebd97510 7875932a ff53d53e
decc7ea2 b44ddbad e49c17d1 d8430bc9
8c94b7bc 8b7d4b4b 3927f67d 1669a432
Poly1305 Key:
000 7b ac 2b 25 2d b4 47 af 09 b6 7a 55 a4 e9 55 84 {.+%-.G...zU..U.
016 0a e1 d6 73 10 75 d9 eb 2a 93 75 78 3e d5 53 ff ...s.u..*.ux>.S.
Poly1305 r = 455e9a4057ab6080f47b42c052bac7b
Poly1305 s = ff53d53e7875932aebd9751073d6e10a
keystream bytes:
9f:7b:e9:5d:01:fd:40:ba:15:e2:8f:fb:36:81:0a:ae:
c1:c0:88:3f:09:01:6e:de:dd:8a:d0:87:55:82:03:a5:
4e:9e:cb:38:ac:8e:5e:2b:b8:da:b2:0f:fa:db:52:e8:
75:04:b2:6e:be:69:6d:4f:60:a4:85:cf:11:b8:1b:59:
fc:b1:c4:5f:42:19:ee:ac:ec:6a:de:c3:4e:66:69:78:
8e:db:41:c4:9c:a3:01:e1:27:e0:ac:ab:3b:44:b9:cf:
5c:86:bb:95:e0:6b:0d:f2:90:1a:b6:45:e4:ab:e6:22:
15:38
Ciphertext:
000 d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2 ...4d.`.{...S.~.
016 a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6 ...Q)n......6.b.
032 3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b =..^..g....i..r.
048 1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36 .q.....)....~.;6
064 92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58 ....-w......(..X
080 fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc ..$...u.U...H1..
096 3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b ?....Kz..v.e...K
112 61 16 a.
AEAD Construction for Poly1305:
000 50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 00 00 00 00 PQRS............
016 d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2 ...4d.`.{...S.~.
032 a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6 ...Q)n......6.b.
048 3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b =..^..g....i..r.
064 1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36 .q.....)....~.;6
080 92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58 ....-w......(..X
096 fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc ..$...u.U...H1..
112 3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b ?....Kz..v.e...K
128 61 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 a...............
144 0c 00 00 00 00 00 00 00 72 00 00 00 00 00 00 00 ........r.......
Note the four zero bytes in line 000 and the 14 zero bytes in line
128
Tag: 1a:e1:0b:59:4f:09:e2:6a:7e:90:2e:cb:d0:60:06:91
(page 24 continued on part 2)
