| Crypto Forum | Y. Nir |
| Internet-Draft | Dell EMC |
| Obsoletes: 7539 (if approved) | A. Langley |
| Intended status: Informational | Google, Inc. |
| Expires: September 30, 2018 | March 29, 2018 |
ChaCha20 and Poly1305 for IETF Protocols
draft-nir-cfrg-rfc7539bis-04
This document defines the ChaCha20 stream cipher as well as the use of the Poly1305 authenticator, both as stand-alone algorithms and as a "combined mode", or Authenticated Encryption with Associated Data (AEAD) algorithm.
RFC 7539, the predecessor of this document, was meant to serve as a stable reference and an implementation guide. It was a product of the Crypto Forum Research Group (CFRG). This document merges the errata filed against RFC 7539 and adds a little text to the Security Considerations section.
This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."
This Internet-Draft will expire on September 30, 2018.
Copyright (c) 2018 IETF Trust and the persons identified as the document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.
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:
This document and its predecesor do not introduce these new algorithms for the first time. They have been defined in scientific papers by D. J. Bernstein. [ChaCha][Poly1305] The purpose of this document is to serve as a stable reference for IETF documents making use of these algorithms.
These algorithms have undergone rigorous analysis. Several papers discuss the security of Salsa and ChaCha ([LatinDances], [LatinDances2], [Zhenqing2012]).
This document represents the consensus of the Crypto Forum Research Group (CFRG). It replaces [RFC7539].
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.
The description of the ChaCha algorithm will at various time refer to the ChaCha state as a "vector" or as a "matrix". This follows the use of these terms in [ChaCha]. The matrix notation is more visually convenient and gives a better notion as to why some rounds are called "column rounds" while others are called "diagonal rounds". Here's a diagram of how the matrices relate to vectors (using the C language convention of zero being the index origin).
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The elements in this vector or matrix are 32-bit unsigned integers.
The algorithm name is "ChaCha". "ChaCha20" is a specific instance where 20 "rounds" (or 80 quarter rounds -- see Section 2.1) are used. Other variations are defined, with 8 or 12 rounds, but in this document we only describe the 20-round ChaCha, so the names "ChaCha" and "ChaCha20" will be used interchangeably.
The subsections below describe the algorithms used and the AEAD construction.
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):
For example, let's see the add, XOR, and roll operations from the fourth line with sample numbers:
For a test vector, we will use the same numbers as in the example, adding something random for c.
After running a Quarter Round on these four numbers, we get these:
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".
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.
The ChaCha block function transforms a ChaCha state by running multiple quarter rounds.
The inputs to ChaCha20 are:
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:
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:
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.
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
initial_state = state
for i=1 upto 10
inner_block(state)
end
state += initial_state
return serialize(state)
end
Where the pipe character ("|") denotes concatenation.
For a test vector, we will use the following inputs to the ChaCha20 block function:
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<N
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:
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.
chacha20_encrypt(key, counter, nonce, plaintext):
for j = 0 upto floor(len(plaintext)/64)-1
key_stream = chacha20_block(key, counter+j, nonce)
block = plaintext[(j*64)..(j*64+63)]
encrypted_message += block ^ key_stream
end
if ((len(plaintext) % 64) != 0)
j = floor(len(plaintext)/64)
key_stream = chacha20_block(key, counter+j, nonce)
block = plaintext[(j*64)..len(plaintext)-1]
encrypted_message += (block^key_stream)[0..len(plaintext)%64]
end
return encrypted_message
end
For a test vector, we will use the following inputs to the ChaCha20 block function:
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:
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 .M
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):
The following sample code clamps "r" to be appropriate:
/*
Adapted from poly1305aes_test_clamp.c version 20050207
D. J. Bernstein
Public domain.
*/
#include "poly1305aes_test.h"
void poly1305aes_test_clamp(unsigned char r[16])
{
r[3] &= 15;
r[7] &= 15;
r[11] &= 15;
r[15] &= 15;
r[4] &= 252;
r[8] &= 252;
r[12] &= 252;
}
Where "&=" is the C language bitwise AND assignment operator.
The "s" should be unpredictable, but it is perfectly acceptable to generate both "r" and "s" uniquely each time. Because each of them is 128 bits, pseudorandomly generating them (see Section 2.6) is also acceptable.
The inputs to Poly1305 are:
The output is a 128-bit tag.
First, the "r" value is clamped.
Next, set the constant prime "P" be 2^130-5: 3fffffffffffffffffffffffffffffffb. Also set a variable "accumulator" to zero.
Next, divide the message into 16-byte blocks. The last one might be shorter:
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.
clamp(r): r &= 0x0ffffffc0ffffffc0ffffffc0fffffff
poly1305_mac(msg, key):
r = le_bytes_to_num(key[0..15])
clamp(r)
s = le_bytes_to_num(key[16..31])
a = 0 /* a is the accumulator */
p = (1<<130)-5
for i=1 upto ceil(msg length in bytes / 16)
n = le_bytes_to_num(msg[((i-1)*16)..(i*16)] | [0x01])
a += n
a = (r * a) % p
end
a += s
return num_to_16_le_bytes(a)
end
For our example, we will dispense with generating the one-time key using AES, and assume that we got the following keying material:
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:a9
As said in Section 2.5, it is acceptable to generate the one-time Poly1305 key pseudorandomly. This section defines such a method.
To generate such a key pair (r,s), we will use the ChaCha20 block function described in Section 2.3. This assumes that we have a 256-bit session key specifically for the Message Authentication Code (MAC) function. Any document that specifies the use of Poly1305 as a MAC algorithm for some protocol MUST specify that 256 bits are allocated for the integrity key. Note that in the AEAD construction defined in Section 2.8, the same key is used for encryption and key generation.
The method is to call the block function with the following parameters:
After running the block function, we have a 512-bit state. We take the first 256 bits of the serialized state, and use those as the one-time Poly1305 key: the first 128 bits are clamped and form "r", while the next 128 bits become "s". The other 256 bits are discarded.
Note that while many protocols have provisions for a nonce for encryption algorithms (often called Initialization Vectors, or IVs), they usually don't have such a provision for the MAC function. In that case, the per-invocation nonce will have to come from somewhere else, such as a message counter.
poly1305_key_gen(key,nonce):
counter = 0
block = chacha20_block(key,counter,nonce)
return block[0..31]
end
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.
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.
AEAD_CHACHA20_POLY1305 is an authenticated encryption with additional data algorithm. The inputs to AEAD_CHACHA20_POLY1305 are:
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:
The output from the AEAD is the concatenation of:
Decryption is similar with the following differences:
A few notes about this design:
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:
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.
pad16(x):
if (len(x) % 16)==0
then return NULL
else return copies(0, 16-(len(x)%16))
end
chacha20_aead_encrypt(aad, key, iv, constant, plaintext):
nonce = constant | iv
otk = poly1305_key_gen(key, nonce)
ciphertext = chacha20_encrypt(key, 1, nonce, plaintext)
mac_data = aad | pad16(aad)
mac_data |= ciphertext | pad16(ciphertext)
mac_data |= num_to_8_le_bytes(aad.length)
mac_data |= num_to_8_le_bytes(ciphertext.length)
tag = poly1305_mac(mac_data, otk)
return (ciphertext, tag)
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
Each block of ChaCha20 involves 16 move operations and one increment operation for loading the state, 80 each of XOR, addition and roll operations for the rounds, 16 more add operations and 16 XOR operations for protecting the plaintext. Section 2.3 describes the ChaCha block function as "adding the original input words". This implies that before starting the rounds on the ChaCha state, we copy it aside, only to add it in later. This is correct, but we can save a few operations if we instead copy the state and do the work on the copy. This way, for the next block you don't need to recreate the state, but only to increment the block counter. This saves approximately 5.5% of the cycles.
It is not recommended to use a generic big number library such as the one in OpenSSL for the arithmetic operations in Poly1305. Such libraries use dynamic allocation to be able to handle an integer of any size, but that flexibility comes at the expense of performance as well as side-channel security. More efficient implementations that run in constant time are available, one of them in D. J. Bernstein's own library, NaCl ([NaCl]). A constant-time but not optimal approach would be to naively implement the arithmetic operations for 288-bit integers, because even a naive implementation will not exceed 2^288 in the multiplication of (acc+block) and r. An efficient constant-time implementation can be found in the public domain library poly1305-donna ([Poly1305_Donna]).
The ChaCha20 cipher is designed to provide 256-bit security.
The Poly1305 authenticator is designed to ensure that forged messages are rejected with a probability of 1-(n/(2^102)) for a 16n-byte message, even after sending 2^64 legitimate messages, so it is SUF‑CMA (strong unforgeability against chosen-message attacks) in the terminology of [AE].
Proving the security of either of these is beyond the scope of this document. Such proofs are available in the referenced academic papers ([ChaCha], [Poly1305], [LatinDances], [LatinDances2], and [Zhenqing2012]).
The most important security consideration in implementing this document is the uniqueness of the nonce used in ChaCha20. Counters and LFSRs are both acceptable ways of generating unique nonces, as is encrypting a counter using a block cipher with a 64-bit block size such as DES. Note that it is not acceptable to use a truncation of a counter encrypted with block ciphers with 128-bit or 256-bit blocks, because such a truncation may repeat after a short time.
Consequences of repeating a nonce: If a nonce is repeated, then both the one-time Poly1305 key and the keystream are identical between the messages. This reveals the XOR of the plaintexts, because the XOR of the plaintexts is equal to the XOR of the ciphertexts.
The Poly1305 key MUST be unpredictable to an attacker. Randomly generating the key would fulfill this requirement, except that Poly1305 is often used in communications protocols, so the receiver should know the key. Pseudorandom number generation such as by encrypting a counter is acceptable. Using ChaCha with a secret key and a nonce is also acceptable.
The algorithms presented here were designed to be easy to implement in constant time to avoid side-channel vulnerabilities. The operations used in ChaCha20 are all additions, XORs, and fixed rolls. All of these can and should be implemented in constant time. Access to offsets into the ChaCha state and the number of operations do not depend on any property of the key, eliminating the chance of information about the key leaking through the timing of cache misses.
For Poly1305, the operations are addition, multiplication. and modulus, all on numbers with greater than 128 bits. This can be done in constant time, but a naive implementation (such as using some generic big number library) will not be constant time. For example, if the multiplication is performed as a separate operation from the modulus, the result will sometimes be under 2^256 and sometimes be above 2^256. Implementers should be careful about timing side-channels for Poly1305 by using the appropriate implementation of these operations.
Validating the authenticity of a message involves a bitwise comparison of the calculated tag with the received tag. In most use cases, nonces and AAD contents are not "used up" until a valid message is received. This allows an attacker to send multiple identical messages with different tags until one passes the tag comparison. This is hard if the attacker has to try all 2^128 possible tags one by one. However, if the timing of the tag comparison operation reveals how long a prefix of the calculated and received tags is identical, the number of messages can be reduced significantly. For this reason, with online protocols, implementation MUST use a constant-time comparison function rather than relying on optimized but insecure library functions such as the C language's memcmp().
Additionally, any protocol using this algorithm MUST include the complete tag to minimize the opportunity for forgery. Tag truncation MUST NOT be done.
IANA has assigned an entry in the "Authenticated Encryption with Associated Data (AEAD) Parameters" registry with 29 as the Numeric ID, "AEAD_CHACHA20_POLY1305" as the name, and RFC 7539 as reference.
IANA is requested to modify the registry by using this document as reference.
| [ChaCha] | Bernstein, D., "ChaCha, a variant of Salsa20", January 2008. |
| [Poly1305] | Bernstein, D., "The Poly1305-AES message-authentication code", March 2005. |
| [RFC2119] | Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997. |
| [RFC8174] | Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017. |
The subsections of this appendix contain more test vectors for the algorithms in the sub-sections of Section 2.
Test Vector #1:
==============
Key:
000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
Nonce:
000 00 00 00 00 00 00 00 00 00 00 00 00 ............
Block Counter = 0
ChaCha state at the end
ade0b876 903df1a0 e56a5d40 28bd8653
b819d2bd 1aed8da0 ccef36a8 c70d778b
7c5941da 8d485751 3fe02477 374ad8b8
f4b8436a 1ca11815 69b687c3 8665eeb2
Keystream:
000 76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28 v.....=.@]j.S..(
016 bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7 .........6...w..
032 da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37 .AY|QWH.w$.?..J7
048 6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86 jC.........i..e.
Test Vector #2:
==============
Key:
000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
Nonce:
000 00 00 00 00 00 00 00 00 00 00 00 00 ............
Block Counter = 1
ChaCha state at the end
bee7079f 7a385155 7c97ba98 0d082d73
a0290fcb 6965e348 3e53c612 ed7aee32
7621b729 434ee69c b03371d5 d539d874
281fed31 45fb0a51 1f0ae1ac 6f4d794b
Keystream:
000 9f 07 e7 be 55 51 38 7a 98 ba 97 7c 73 2d 08 0d ....UQ8z...|s-..
016 cb 0f 29 a0 48 e3 65 69 12 c6 53 3e 32 ee 7a ed ..).H.ei..S>2.z.
032 29 b7 21 76 9c e6 4e 43 d5 71 33 b0 74 d8 39 d5 ).!v..NC.q3.t.9.
048 31 ed 1f 28 51 0a fb 45 ac e1 0a 1f 4b 79 4d 6f 1..(Q..E....KyMo
Test Vector #3:
==============
Key:
000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 ................
Nonce:
000 00 00 00 00 00 00 00 00 00 00 00 00 ............
Block Counter = 1
ChaCha state at the end
2452eb3a 9249f8ec 8d829d9b ddd4ceb1
e8252083 60818b01 f38422b8 5aaa49c9
bb00ca8e da3ba7b4 c4b592d1 fdf2732f
4436274e 2561b3c8 ebdd4aa6 a0136c00
Keystream:
000 3a eb 52 24 ec f8 49 92 9b 9d 82 8d b1 ce d4 dd :.R$..I.........
016 83 20 25 e8 01 8b 81 60 b8 22 84 f3 c9 49 aa 5a . %....`."...I.Z
032 8e ca 00 bb b4 a7 3b da d1 92 b5 c4 2f 73 f2 fd ......;...../s..
048 4e 27 36 44 c8 b3 61 25 a6 4a dd eb 00 6c 13 a0 N'6D..a%.J...l..
Test Vector #4:
==============
Key:
000 00 ff 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
Nonce:
000 00 00 00 00 00 00 00 00 00 00 00 00 ............
Block Counter = 2
ChaCha state at the end
fb4dd572 4bc42ef1 df922636 327f1394
a78dea8f 5e269039 a1bebbc1 caf09aae
a25ab213 48a6b46c 1b9d9bcb 092c5be6
546ca624 1bec45d5 87f47473 96f0992e
Keystream:
000 72 d5 4d fb f1 2e c4 4b 36 26 92 df 94 13 7f 32 r.M....K6&.....2
016 8f ea 8d a7 39 90 26 5e c1 bb be a1 ae 9a f0 ca ....9.&^........
032 13 b2 5a a2 6c b4 a6 48 cb 9b 9d 1b e6 5b 2c 09 ..Z.l..H.....[,.
048 24 a6 6c 54 d5 45 ec 1b 73 74 f4 87 2e 99 f0 96 $.lT.E..st......
Test Vector #5:
==============
Key:
000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
Nonce:
000 00 00 00 00 00 00 00 00 00 00 00 02 ............
Block Counter = 0
ChaCha state at the end
374dc6c2 3736d58c b904e24a cd3f93ef
88228b1a 96a4dfb3 5b76ab72 c727ee54
0e0e978a f3145c95 1b748ea8 f786c297
99c28f5f 628314e8 398a19fa 6ded1b53
Keystream:
000 c2 c6 4d 37 8c d5 36 37 4a e2 04 b9 ef 93 3f cd ..M7..67J.....?.
016 1a 8b 22 88 b3 df a4 96 72 ab 76 5b 54 ee 27 c7 ..".....r.v[T.'.
032 8a 97 0e 0e 95 5c 14 f3 a8 8e 74 1b 97 c2 86 f7 .....\....t.....
048 5f 8f c2 99 e8 14 83 62 fa 19 8a 39 53 1b ed 6d _......b...9S..m
Test Vector #1: ============== Key: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ Nonce: 000 00 00 00 00 00 00 00 00 00 00 00 00 ............ Initial Block Counter = 0 Plaintext: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 032 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 048 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ Ciphertext: 000 76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28 v.....=.@]j.S..( 016 bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7 .........6...w.. 032 da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37 .AY|QWH.w$.?..J7 048 6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86 jC.........i..e.
Test Vector #2:
==============
Key:
000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 ................
Nonce:
000 00 00 00 00 00 00 00 00 00 00 00 02 ............
Initial Block Counter = 1
Plaintext:
000 41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74 Any submission t
016 6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e o the IETF inten
032 64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72 ded by the Contr
048 69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69 ibutor for publi
064 63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72 cation as all or
080 20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46 part of an IETF
096 20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20 Internet-Draft
112 6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73 or RFC and any s
128 74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69 tatement made wi
144 74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74 thin the context
160 20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69 of an IETF acti
176 76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72 vity is consider
192 65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74 ed an "IETF Cont
208 72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20 ribution". Such
224 73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75 statements inclu
240 64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e de oral statemen
256 74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69 ts in IETF sessi
272 6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20 ons, as well as
288 77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63 written and elec
304 74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61 tronic communica
320 74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e tions made at an
336 79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c y time or place,
352 20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65 which are addre
368 73 73 65 64 20 74 6f ssed to
Ciphertext:
000 a3 fb f0 7d f3 fa 2f de 4f 37 6c a2 3e 82 73 70 ...}../.O7l.>.sp
016 41 60 5d 9f 4f 4f 57 bd 8c ff 2c 1d 4b 79 55 ec A`].OOW...,.KyU.
032 2a 97 94 8b d3 72 29 15 c8 f3 d3 37 f7 d3 70 05 *....r)....7..p.
048 0e 9e 96 d6 47 b7 c3 9f 56 e0 31 ca 5e b6 25 0d ....G...V.1.^.%.
064 40 42 e0 27 85 ec ec fa 4b 4b b5 e8 ea d0 44 0e @B.'....KK....D.
080 20 b6 e8 db 09 d8 81 a7 c6 13 2f 42 0e 52 79 50 ........./B.RyP
096 42 bd fa 77 73 d8 a9 05 14 47 b3 29 1c e1 41 1c B..ws....G.)..A.
112 68 04 65 55 2a a6 c4 05 b7 76 4d 5e 87 be a8 5a h.eU*....vM^...Z
128 d0 0f 84 49 ed 8f 72 d0 d6 62 ab 05 26 91 ca 66 ...I..r..b..&..f
144 42 4b c8 6d 2d f8 0e a4 1f 43 ab f9 37 d3 25 9d BK.m-....C..7.%.
160 c4 b2 d0 df b4 8a 6c 91 39 dd d7 f7 69 66 e9 28 ......l.9...if.(
176 e6 35 55 3b a7 6c 5c 87 9d 7b 35 d4 9e b2 e6 2b .5U;.l\..{5....+
192 08 71 cd ac 63 89 39 e2 5e 8a 1e 0e f9 d5 28 0f .q..c.9.^.....(.
208 a8 ca 32 8b 35 1c 3c 76 59 89 cb cf 3d aa 8b 6c ..2.5.<vY...=..l
224 cc 3a af 9f 39 79 c9 2b 37 20 fc 88 dc 95 ed 84 .:..9y.+7 ......
240 a1 be 05 9c 64 99 b9 fd a2 36 e7 e8 18 b0 4b 0b ....d....6....K.
256 c3 9c 1e 87 6b 19 3b fe 55 69 75 3f 88 12 8c c0 ....k.;.Uiu?....
272 8a aa 9b 63 d1 a1 6f 80 ef 25 54 d7 18 9c 41 1f ...c..o..%T...A.
288 58 69 ca 52 c5 b8 3f a3 6f f2 16 b9 c1 d3 00 62 Xi.R..?.o......b
304 be bc fd 2d c5 bc e0 91 19 34 fd a7 9a 86 f6 e6 ...-.....4......
320 98 ce d7 59 c3 ff 9b 64 77 33 8f 3d a4 f9 cd 85 ...Y...dw3.=....
336 14 ea 99 82 cc af b3 41 b2 38 4d d9 02 f3 d1 ab .......A.8M.....
352 7a c6 1d d2 9c 6f 21 ba 5b 86 2f 37 30 e3 7c fd z....o!.[./70.|.
368 c4 fd 80 6c 22 f2 21 ...l".!
Test Vector #3: ============== Key: 000 1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0 ..@..U...3...... 016 47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0 G9..@+....\. pu. Nonce: 000 00 00 00 00 00 00 00 00 00 00 00 02 ............ Initial Block Counter = 42 Plaintext: 000 27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61 'Twas brillig, a 016 6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f nd the slithy to 032 76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64 ves.Did gyre and 048 20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77 gimble in the w 064 61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77 abe:.All mimsy w 080 65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65 ere the borogove 096 73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20 s,.And the mome 112 72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e raths outgrabe. Ciphertext: 000 62 e6 34 7f 95 ed 87 a4 5f fa e7 42 6f 27 a1 df b.4....._..Bo'.. 016 5f b6 91 10 04 4c 0d 73 11 8e ff a9 5b 01 e5 cf _....L.s....[... 032 16 6d 3d f2 d7 21 ca f9 b2 1e 5f b1 4c 61 68 71 .m=..!...._.Lahq 048 fd 84 c5 4f 9d 65 b2 83 19 6c 7f e4 f6 05 53 eb ...O.e...l....S. 064 f3 9c 64 02 c4 22 34 e3 2a 35 6b 3e 76 43 12 a6 ..d.."4.*5k>vC.. 080 1a 55 32 05 57 16 ea d6 96 25 68 f8 7d 3f 3f 77 .U2.W....%h.}??w 096 04 c6 a8 d1 bc d1 bf 4d 50 d6 15 4b 6d a7 31 b1 .......MP..Km.1. 112 87 b5 8d fd 72 8a fa 36 75 7a 79 7a c1 88 d1 ....r..6uzyz...
Notice how, in test vector #2, r is equal to zero. The part of the Poly1305 algorithm where the accumulator is multiplied by r means that with r equal zero, the tag will be equal to s regardless of the content of the text. Fortunately, all the proposed methods of generating r are such that getting this particular weak key is very unlikely.
Test Vector #1: ============== One-time Poly1305 Key: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ Text to MAC: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 032 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 048 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ Tag: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
Test Vector #2: ============== One-time Poly1305 Key: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 016 36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e 6.....`p...."z.> Text to MAC: 000 41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74 Any submission t 016 6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e o the IETF inten 032 64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72 ded by the Contr 048 69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69 ibutor for publi 064 63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72 cation as all or 080 20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46 part of an IETF 096 20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20 Internet-Draft 112 6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73 or RFC and any s 128 74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69 tatement made wi 144 74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74 thin the context 160 20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69 of an IETF acti 176 76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72 vity is consider 192 65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74 ed an "IETF Cont 208 72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20 ribution". Such 224 73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75 statements inclu 240 64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e de oral statemen 256 74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69 ts in IETF sessi 272 6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20 ons, as well as 288 77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63 written and elec 304 74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61 tronic communica 320 74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e tions made at an 336 79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c y time or place, 352 20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65 which are addre 368 73 73 65 64 20 74 6f ssed to Tag: 000 36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e 6.....`p...."z.>
Test Vector #3: ============== One-time Poly1305 Key: 000 36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e 6.....`p...."z.> 016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ Text to MAC: 000 41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74 Any submission t 016 6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e o the IETF inten 032 64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72 ded by the Contr 048 69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69 ibutor for publi 064 63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72 cation as all or 080 20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46 part of an IETF 096 20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20 Internet-Draft 112 6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73 or RFC and any s 128 74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69 tatement made wi 144 74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74 thin the context 160 20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69 of an IETF acti 176 76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72 vity is consider 192 65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74 ed an "IETF Cont 208 72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20 ribution". Such 224 73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75 statements inclu 240 64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e de oral statemen 256 74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69 ts in IETF sessi 272 6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20 ons, as well as 288 77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63 written and elec 304 74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61 tronic communica 320 74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e tions made at an 336 79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c y time or place, 352 20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65 which are addre 368 73 73 65 64 20 74 6f ssed to Tag: 000 f3 47 7e 7c d9 54 17 af 89 a6 b8 79 4c 31 0c f0 .G~|.T.....yL1..
Test Vector #4: ============== One-time Poly1305 Key: 000 1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0 ..@..U...3...... 016 47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0 G9..@+....\. pu. Text to MAC: 000 27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61 'Twas brillig, a 016 6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f nd the slithy to 032 76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64 ves.Did gyre and 048 20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77 gimble in the w 064 61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77 abe:.All mimsy w 080 65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65 ere the borogove 096 73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20 s,.And the mome 112 72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e raths outgrabe. Tag: 000 45 41 66 9a 7e aa ee 61 e7 08 dc 7c bc c5 eb 62 EAf.~..a...|...b
Test Vector #5: If one uses 130-bit partial reduction, does the code handle the case where partially reduced final result is not fully reduced?
R: 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 S: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 data: FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF tag: 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Test Vector #6: What happens if addition of s overflows modulo 2^128?
R: 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 S: FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF data: 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 tag: 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Test Vector #7: What happens if data limb is all ones and there is carry from lower limb?
R: 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 S: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 data: FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF F0 FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 tag: 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Test Vector #8: What happens if final result from polynomial part is exactly 2^130-5?
R: 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 S: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 data: FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FB FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 tag: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Test Vector #9: What happens if final result from polynomial part is exactly 2^130-6?
R: 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 S: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 data: FD FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF tag: FA FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
Test Vector #10: What happens if 5*H+L-type reduction produces 131-bit intermediate result?
R: 01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00 S: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 data: E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00 33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 tag: 14 00 00 00 00 00 00 00 55 00 00 00 00 00 00 00
Test Vector #11: What happens if 5*H+L-type reduction produces 131-bit final result?
R: 01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00 S: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 data: E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00 33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 tag: 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Test Vector #1: ============== The ChaCha20 Key: 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ 016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................ The nonce: 000 00 00 00 00 00 00 00 00 00 00 00 00 ............ Poly1305 one-time key: 000 76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28 v.....=.@]j.S..( 016 bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7 .........6...w..
Test Vector #2:
==============
The ChaCha20 Key
000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................
016 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 ................
The nonce:
000 00 00 00 00 00 00 00 00 00 00 00 02 ............
Poly1305 one-time key:
000 ec fa 25 4f 84 5f 64 74 73 d3 cb 14 0d a9 e8 76 ..%O._dts......v
016 06 cb 33 06 6c 44 7b 87 bc 26 66 dd e3 fb b7 39 ..3.lD{..&f....9
Test Vector #3: ============== The ChaCha20 Key 000 1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0 ..@..U...3...... 016 47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0 G9..@+....\. pu. The nonce: 000 00 00 00 00 00 00 00 00 00 00 00 02 ............ Poly1305 one-time key: 000 96 5e 3b c6 f9 ec 7e d9 56 08 08 f4 d2 29 f9 4b .^;...~.V....).K 016 13 7f f2 75 ca 9b 3f cb dd 59 de aa d2 33 10 ae ...u..?..Y...3..
Below we see decrypting a message. We receive a ciphertext, a nonce, and a tag. We know the key. We will check the tag and then (assuming that it validates) decrypt the ciphertext. In this particular protocol, we'll assume that there is no padding of the plaintext.
The ChaCha20 Key
000 1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0 ..@..U...3......
016 47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0 G9..@+....\. pu.
Ciphertext:
000 64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd d...u...`.b...C.
016 5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2 ^.\.4\....g..l..
032 4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0 Ll..u]C....N8-&.
048 bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf ...<2.....;.5X..
064 33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81 3/..q......J....
080 14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55 ...n..3.`....7.U
096 97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38 ...n...a..2N+5.8
112 36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4 6..{j|.....{S.g.
128 b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9 ..lv{.MF..R.....
144 90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e .@...3"^.....lR>
160 af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a .E4..?..[.Gq..Tj
176 0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a ..+..VN..B"s.H'.
192 0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e ..1`S.v..U..1YCN
208 ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10 ..NFm.Z.s.rv'.z.
224 49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30 I....6...h..w.q0
240 30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29 0[.......{qMlo,)
256 a6 ad 5c b4 02 2b 02 70 9b ..\..+.p.
The nonce:
000 00 00 00 00 01 02 03 04 05 06 07 08 ............
The AAD:
000 f3 33 88 86 00 00 00 00 00 00 4e 91 .3........N.
Received Tag:
000 ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38 ...g..."9#6....8
First, we calculate the one-time Poly1305 key
ChaCha state with key setup
61707865 3320646e 79622d32 6b206574
a540921c 8ad355eb 868833f3 f0b5f604
c1173947 09802b40 bc5cca9d c0757020
00000000 00000000 04030201 08070605
ChaCha state after 20 rounds
a94af0bd 89dee45c b64bb195 afec8fa1
508f4726 63f554c0 1ea2c0db aa721526
11b1e514 a0bacc0f 828a6015 d7825481
e8a4a850 d9dcbbd6 4c2de33a f8ccd912
out bytes:
bd:f0:4a:a9:5c:e4:de:89:95:b1:4b:b6:a1:8f:ec:af:
26:47:8f:50:c0:54:f5:63:db:c0:a2:1e:26:15:72:aa
Poly1305 one-time key:
000 bd f0 4a a9 5c e4 de 89 95 b1 4b b6 a1 8f ec af ..J.\.....K.....
016 26 47 8f 50 c0 54 f5 63 db c0 a2 1e 26 15 72 aa &G.P.T.c....&.r.
Next, we construct the AEAD buffer
Poly1305 Input:
000 f3 33 88 86 00 00 00 00 00 00 4e 91 00 00 00 00 .3........N.....
016 64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd d...u...`.b...C.
032 5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2 ^.\.4\....g..l..
048 4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0 Ll..u]C....N8-&.
064 bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf ...<2.....;.5X..
080 33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81 3/..q......J....
096 14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55 ...n..3.`....7.U
112 97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38 ...n...a..2N+5.8
128 36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4 6..{j|.....{S.g.
144 b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9 ..lv{.MF..R.....
160 90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e .@...3"^.....lR>
176 af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a .E4..?..[.Gq..Tj
192 0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a ..+..VN..B"s.H'.
208 0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e ..1`S.v..U..1YCN
224 ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10 ..NFm.Z.s.rv'.z.
240 49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30 I....6...h..w.q0
256 30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29 0[.......{qMlo,)
272 a6 ad 5c b4 02 2b 02 70 9b 00 00 00 00 00 00 00 ..\..+.p........
288 0c 00 00 00 00 00 00 00 09 01 00 00 00 00 00 00 ................
We calculate the Poly1305 tag and find that it matches
Calculated Tag: 000 ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38 ...g..."9#6....8
Finally, we decrypt the ciphertext
Plaintext:: 000 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 73 20 Internet-Drafts 016 61 72 65 20 64 72 61 66 74 20 64 6f 63 75 6d 65 are draft docume 032 6e 74 73 20 76 61 6c 69 64 20 66 6f 72 20 61 20 nts valid for a 048 6d 61 78 69 6d 75 6d 20 6f 66 20 73 69 78 20 6d maximum of six m 064 6f 6e 74 68 73 20 61 6e 64 20 6d 61 79 20 62 65 onths and may be 080 20 75 70 64 61 74 65 64 2c 20 72 65 70 6c 61 63 updated, replac 096 65 64 2c 20 6f 72 20 6f 62 73 6f 6c 65 74 65 64 ed, or obsoleted 112 20 62 79 20 6f 74 68 65 72 20 64 6f 63 75 6d 65 by other docume 128 6e 74 73 20 61 74 20 61 6e 79 20 74 69 6d 65 2e nts at any time. 144 20 49 74 20 69 73 20 69 6e 61 70 70 72 6f 70 72 It is inappropr 160 69 61 74 65 20 74 6f 20 75 73 65 20 49 6e 74 65 iate to use Inte 176 72 6e 65 74 2d 44 72 61 66 74 73 20 61 73 20 72 rnet-Drafts as r 192 65 66 65 72 65 6e 63 65 20 6d 61 74 65 72 69 61 eference materia 208 6c 20 6f 72 20 74 6f 20 63 69 74 65 20 74 68 65 l or to cite the 224 6d 20 6f 74 68 65 72 20 74 68 61 6e 20 61 73 20 m other than as 240 2f e2 80 9c 77 6f 72 6b 20 69 6e 20 70 72 6f 67 /...work in prog 256 72 65 73 73 2e 2f e2 80 9d ress./...
The following measurements were made by Adam Langley for a blog post published on February 27th, 2014. The original blog post was available at the time of this writing at <https://www.imperialviolet.org/2014/02/27/tlssymmetriccrypto.html>.
| Chip | AES-128-GCM | ChaCha20-Poly1305 |
|---|---|---|
| OMAP 4460 | 24.1 MB/s | 75.3 MB/s |
| Snapdragon S4 Pro | 41.5 MB/s | 130.9 MB/s |
| Sandy Bridge Xeon (AES-NI) | 900 MB/s | 500 MB/s |
ChaCha20 and Poly1305 were invented by Daniel J. Bernstein. The AEAD construction and the method of creating the one-time Poly1305 key were invented by Adam Langley.
Thanks to Robert Ransom, Watson Ladd, Stefan Buhler, Dan Harkins, and Kenny Paterson for their helpful comments and explanations. Thanks to Niels Moller for suggesting the more efficient AEAD construction in this document. Special thanks to Ilari Liusvaara for providing extra test vectors, helpful comments, and for being the first to attempt an implementation from this document. Thanks to Sean Parkinson for suggesting improvements to the examples and the pseudocode. Thanks to David Ireland for pointing out a bug in the pseudocode, and to Stephen Farrell and Alyssa Rowan for pointing out missing advise in the security considerations.
Special thanks goes to Gordon Procter for performing a security analysis of the composition and publishing [Procter].
Jim Schaad and John Mattson provided feedback on tag truncation, and Russ Housley, Stanislav Smyshlyaev and John Mattson each provided a review of this version.