Salsa20

Salsa20

The Salsa quarter-round function. Four parallel copies make a round.
General
Designers	Daniel J. Bernstein
First published	2007 (designed 2005)
Related to	Rumba20, ChaCha
Certification	eSTREAM portfolio
Cipher detail
Key sizes	256 bits
State size	512 bits
Structure	ARX
Rounds	20
Speed	3.91 cpb on an Intel Core 2 Duo
Best public cryptanalysis
2008 cryptanalysis breaks 8 out of 20 rounds to recover the 256-bit secret key in 2251 operations, using 231 keystream pairs.

Salsa20 and the closely related ChaCha are stream ciphers developed by Daniel J. Bernstein. Because the two ciphers are very similar, this article will some times discuss them together. Salsa20 is the original cipher, and it was submitted to eSTREAM by Daniel J. Bernstein. ChaCha is a modification of Salsa20 published by Bernstein in 2008. It uses a new round function that increases diffusion and increases performance on some architectures.

Both ciphers are built on a pseudorandom function based on add-rotate-xor (ARX) operations — 32-bit addition, bitwise addition (XOR) and rotation operations. The core function maps a 256-bit key, a 64-bit nonce, and a 64-bit counter to a 512-bit block of the key stream (a Salsa version with a 128-bit key also exists). This gives Salsa20 and ChaCha the unusual advantage that the user can efficiently seek to any position in the key stream in constant time. Salsa20 offers speeds of around 4–14 cycles per byte in software on modern x86 processors, and reasonable hardware performance. It is not patented, and Bernstein has written several public domain implementations optimized for common architectures.

Structure

Internally, the cipher uses bitwise addition ⊕ (exclusive OR), 32-bit addition mod 2³² ⊞, and constant-distance rotation operations (<<<) on an internal state of sixteen 32-bit words. Using only add-rotate-xor operations avoids the possibility of timing attacks in software implementations. The internal state is made of sixteen 32-bit words arranged as a 4x4 matrix.

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

The initial state is made up of 8 words of key, 2 words of stream position, 2 words of nonce (essentially additional stream position bits), and 4 fixed words:

Initial state of Salsa20

Cons	Key	Key	Key
Key	Cons	Nonce	Nonce
Pos	Pos	Cons	Key
Key	Key	Key	Cons

The constant words spell "expand 32-byte k" in ASCII (i.e. the 4 words are "expa", "nd 3", "2-by", and "te k"). This is an example of a nothing up my sleeve number. The core operation in Salsa20 is the quarter-round QR(a,b,c,d) that takes a four-word input and produces a four-word output:

b ⊕= (a ⊞ d) <<< 7;
c ⊕= (b ⊞ a) <<< 9;
d ⊕= (c ⊞ b) <<< 13;
a ⊕= (d ⊞ c) <<< 18;

Odd-numbered rounds apply QR(a,b,c,d) to each of the four columns in the 4x4 matrix, and even-numbered rounds apply it to each of the four rows. Two consecutive rounds (column-round and row-round) together are called a double-round:

// Odd round.
QR( 0,  4,  8, 12) // column 1
QR( 5,  9, 13,  1) // column 2
QR(10, 14,  2,  6) // column 3
QR(15,  3,  7, 11) // column 4
// Even round.
QR( 0,  1,  2,  3) // row 1
QR( 5,  6,  7,  4) // row 2
QR(10, 11,  8,  9) // row 3
QR(15, 12, 13, 14) // row 4

An implementation in C/C++ appears below.

#define ROT(a,b) (((a) << (b)) | ((a) >> (32 - (b))))
#define QR(a, b, c, d)       \
    b ^= ROT(a + d, 7); \
    c ^= ROT(b + a, 9); \
    d ^= ROT(c + b,13); \
    a ^= ROT(d + c,18);

void salsa20_block(uint32 out[16],uint32 in[16])
{
  int i;
  uint32 x[16];
  for (i = 0;i < 16;++i) x[i] = in[i];
  
  // 10 loops x 2 rounds/loop = 20 rounds.
  for (int i = 0; i < 10; i++) {
    // Odd round.
    QR(x[ 0], x[ 4], x[ 8], x[12]) // column 1
    QR(x[ 5], x[ 9], x[13], x[ 1]) // column 2
    QR(x[10], x[14], x[ 2], x[ 6]) // column 3
    QR(x[15], x[ 3], x[ 7], x[11]) // column 4
    // Even round.
    QR(x[ 0], x[ 1], x[ 2], x[ 3]) // row 1
    QR(x[ 5], x[ 6], x[ 7], x[ 4]) // row 2
    QR(x[10], x[11], x[ 8], x[ 9]) // row 3
    QR(x[15], x[12], x[13], x[14]) // row 4
  }
  for (i = 0;i < 16;++i) out[i] = x[i] + in[i];
}

In the last line, the mixed array is added, word by word, to the original array to obtain its 64-byte key stream block. This is important because the mixing rounds on their own are invertible. In other words, applying the reverse operations would produce the original 4x4 matrix, including the key. Adding the mixed array to the original resolves that problem.

Salsa20 performs 20 rounds of mixing on its input. However, reduced round variants Salsa20/8 and Salsa20/12 using 8 and 12 rounds respectively have also been introduced. These variants were introduced to complement the original Salsa20, not to replace it, and perform even better in the eSTREAM benchmarks than Salsa20, though with a correspondingly lower security margin.

In 2008 Bernstein proposed a variant of Salsa20 with 192-bit nonces called XSalsa20. XSalsa20 is provable secure if Salsa20 is secure, but is more suitable for applications where longer nonces are desired.

eSTREAM selection of Salsa20

Salsa20 has been selected as a Phase 3 design for Profile 1 (software) by the eSTREAM project, receiving the highest weighted voting score of any Profile 1 algorithm at the end of Phase 2. Salsa20 had previously been selected as Phase 2 Focus design for Profile 1 (software) and as a Phase 2 design for Profile 2 (hardware) by the eSTREAM project, but was not advanced to Phase 3 for Profile 2 because eSTREAM felt that it was probably not a good candidate for extremely resource constrained hardware environments.

Cryptanalysis of Salsa20

As of 2015, there are no published attacks on Salsa20/12 or the full Salsa20/20; the best attack known breaks 8 of the 12 or 20 rounds.

In 2005, Paul Crowley reported an attack on Salsa20/5 with an estimated time complexity of 2¹⁶⁵, and won Bernstein's US$1000 prize for "most interesting Salsa20 cryptanalysis". This attack, and all subsequent attacks are based on truncated differential cryptanalysis. In 2006, Fischer, Meier, Berbain, Biasse, and Robshaw reported an attack on Salsa20/6 with estimated time complexity of 2¹⁷⁷, and a related-key attack on Salsa20/7 with estimated time complexity of 2²¹⁷.

In 2007, Tsunoo et al. announced a cryptanalysis of Salsa20 which breaks 8 out of 20 rounds to recover the 256-bit secret key in 2²⁵⁵ operations, using 2^11.37 keystream pairs. However, this attack does not seem to be competitive with the brute force attack.

In 2008, Aumasson, Fischer, Khazaei, Meier, and Rechberger reported a cryptanalytic attack against Salsa20/7 with a time complexity of 2¹⁵³, and they reported the first attack against Salsa20/8 with an estimated time complexity of 2²⁵¹. This attack makes use of the new concept of probabilistic neutral key bits for probabilistic detection of a truncated differential. The attack can be adapted to break Salsa20/7 with a 128-bit key.

In 2012 the attack by Aumasson et al. was improved by Shi et al. against Salsa20/7 (128-bit key) to a time complexity of 2¹⁰⁹ and Salsa20/8 (256-bit key) to 2²⁵⁰.

In 2013, Mouha and Preneel published a proof that 15 rounds of Salsa20 was 128-bit secure against differential cryptanalysis. (Specifically, it has no differential characteristic with higher probability than 2⁻¹³⁰, so differential cryptanalysis would be more difficult than 128-bit key exhaustion.)

ChaCha variant

In 2008, Bernstein published the closely related "ChaCha" family of ciphers, which aim to increase the diffusion per round while achieving the same or slightly better performance. The Aumasson et al. paper also attacks ChaCha, achieving one round fewer: for 256 bits ChaCha6 with complexity 2¹³⁹ and ChaCha7 with complexity 2²⁴⁸. 128 bits ChaCha6 within 2¹⁰⁷, but claims that the attack fails to break 128 bits ChaCha7.

Like Salsa20, ChaCha's initial state includes a 128-bit constant, a 256-bit key, a 64-bit counter, and a 64-bit nonce, arranged as a 4x4 matrix of 32-bit words. But ChaCha re-arranges some of the words in the initial state:

Initial state of ChaCha

Cons	Cons	Cons	Cons
Key	Key	Key	Key
Key	Key	Key	Key
Pos	Pos	Nonce	Nonce

The constant is the same as Salsa20 ("expand 32-byte k"). ChaCha replaces the Salsa20 quarter-round QR(a,b,c,d) with

a ⊞= b; d ⊕= a; d <<<= 16;
c ⊞= d; b ⊕= c; b <<<= 12;
a ⊞= b; d ⊕= a; d <<<= 8;
c ⊞= d; b ⊕= c; b <<<= 7;

Notice that this version updates each word twice, while Salsa20's quarter round updates each word only once. In addition, the ChaCha quarter-round diffuses changes more quickly. In average, after changing 1 input bit the Salsa20 quarter-round will change 8 output bits while the ChaCha one will change 12.5 output bits. .

Note also that the ChaCha quarter round has the same number of adds, xors, and bit rotates as the Salsa20 quarter-round, but the fact that two of the rotates are multiples of 8 allows for a small optimization on some architectures including x86. Additionally, the input formatting has been rearranged to support an efficient SSE implementation optimization discovered for Salsa20. Rather than alternating rounds down columns and across rows, they are performed down columns and along diagonals. Like Salsa20, ChaCha arranges the sixteen 32-bit words in a 4x4 matrix. If we index the matrix elements from 0 to 15

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

Then a double round in ChaCha is

// Odd round.
QR(0, 4, 8, 12)   // 1st column
QR(1, 5, 9, 13)   // 2nd column
QR(2, 6, 10, 14)  // 3rd column
QR(3, 7, 11, 15)  // 4th column
// Even round.
QR(0, 5, 10, 15)  // diagonal 1 (main diagonal)
QR(1, 6, 11, 12)  // diagonal 2
QR(2, 7, 8, 13)   // diagonal 3
QR(3, 4, 9, 14)   // diagonal 4

ChaCha20 uses 10 iterations of the double round. An implementation in C/C++ appears below.

#define ROT(a,b) (((a) << (b)) | ((a) >> (32 - (b))))
#define QR(a, b, c, d)       \
   a += b;  d ^= a;  d = ROT(d,16);  \
   c += d;  b ^= c;  b = ROT(b,12);  \
   a += b;  d ^= a;  d = ROT(d, 8);  \
   c += d;  b ^= c;  b = ROT(b, 7)

void chacha_block(uint32 out[16],uint32 in[16])
{
  int i;
  uint32 x[16];
  for (i = 0;i < 16;++i) x[i] = in[i];
  
  // 10 loops x 2 rounds/loop = 20 rounds.
  for (int i = 0; i < 10; i++) {
    // Odd round.
    QR(x[0], x[4], x[ 8], x[12]); // column 0
    QR(x[1], x[5], x[ 9], x[13]); // column 1
    QR(x[2], x[6], x[10], x[14]); // column 2
    QR(x[3], x[7], x[11], x[15]); // column 3
    // Even round.
    QR(x[0], x[5], x[10], x[15]); // diagonal 1 (main diagonal)
    QR(x[1], x[6], x[11], x[12]); // diagonal 2
    QR(x[2], x[7], x[ 8], x[13]); // diagonal 3
    QR(x[3], x[4], x[ 9], x[14]); // diagonal 4
  }
  for (i = 0;i < 16;++i) out[i] = x[i] + in[i];
}

ChaCha is the basis of the BLAKE hash function, a finalist in the NIST hash function competition, and BLAKE2 successor tuned for even higher speed. It also defines a variant using sixteen 64-bit words (1024 bits of state), with correspondingly adjusted rotation constants.

ChaCha20 adoption

Google has selected ChaCha20 along with Bernstein's Poly1305 message authentication code as a replacement for RC4 in TLS, which is used for Internet security. Google's implementation secures https (TLS/SSL) traffic between the Chrome browser on Android phones and Google's websites.

Shortly after Google's adoption for TLS, both the ChaCha20 and Poly1305 algorithms were also used for a new chacha20-poly1305@openssh.com cipher in OpenSSH. Subsequently, this made it possible for OpenSSH to avoid any dependency on OpenSSL, via a compile-time option.

ChaCha20 is also used for the arc4random random number generator in FreeBSD, OpenBSD, and NetBSD operating systems, instead of the broken RC4, and in DragonFly BSD for the CSPRNG subroutine of the kernel. Starting from version 4.8, the Linux kernel uses the ChaCha20 algorithm to generate data for the nonblocking /dev/urandom device.

An implementation reference for ChaCha20 has been published in RFC 7539. The IETF's implementation modified Bernstein's published algorithm by changing 64-bit nonce and 64-bit block counter to 96-bit nonce and 32-bit block counter. The name was not changed when the algorithm was modified and it could be the source of confusion for developers. Because of the reduced block counter, maximum message length that can be safely encrypted by the IETF's variant is 2³²-1 blocks of 64 bytes (about 256 GiB). For usages where this is not enough, such as file or disk encryption, RFC 7539 proposes using the original algorithm with 64-bit nonce.

Use of ChaCha20 in IKE and IPsec have been proposed for standardization in RFC 7634. Proposed standardization of its use in TLS is published as RFC 7905.

See also

• Speck – an add-rotate-xor cipher developed by the NSA

External links

• Snuffle 2005: the Salsa20 encryption function
• Salsa20 specification (PDF)
• Salsa20/8 and Salsa20/12 (PDF)
• The eSTREAM Project: Salsa20
• The ChaCha family of stream ciphers
• Salsa20 Usage & Deployment