Salsa20

Salsa20

The Salsa quarter-round function. Four parallel copies make a round.
General
Designers	Daniel J. Bernstein
Related to	Rumba20, ChaCha
Certification	eSTREAM portfolio
Cipher detail
Key sizes	256 bits
State size	512 bits
Rounds	20
Speed	3.91 cpb on an Intel Core 2 Duo[1]
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.[2]

Salsa20 is a stream cipher submitted to eSTREAM by Daniel J. Bernstein. It is built on a pseudorandom function based on add-rotate-xor (ARX) operations — 32-bit addition, bitwise addition (XOR) and rotation operations. Salsa20 maps a 256-bit key, a 64-bit nonce, and a 64-bit stream position to a 512-bit output (a version with a 128-bit key also exists). This gives Salsa20 the unusual advantage that the user can efficiently seek to any position in the output stream in constant time. It offers speeds of around 4–14 cycles per byte in software on modern x86 processors,^[3] and reasonable hardware performance. It is not patented, and Bernstein has written several public domain implementations optimized for common architectures.^[4] Salsa20 has been submitted to eSTREAM.

A related cipher, ChaCha, which has similar features but a different round function, was published by Bernstein in 2008.

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. This choice of operations avoids the possibility of timing attacks in software implementations. The basic Salsa20 round primitive R(a,b,c,k) is

b ⊕= (a ⊞ c) <<< k;

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. 20 rounds of mixing produce 16 words of stream cipher output.

A quarter-round takes a four-word input and produces a four-word output. The internal 16-word state is arranged as a 4x4 matrix; even-numbered rounds apply the quarter-round operation to each of the four rows, while odd-numbered rounds apply the quarter-round operation to each of the four columns. Two consecutive rounds (a row-round and column-round) together are called a double-round.

A more precise specification appears below as pseudocode, although in this form the row/column pattern is more difficult to see. ⊞ is addition modulo 2³², <<< is the left-rotate operation, and ⊕ is exclusive-or. x ⊕= y is an abbreviation for x = x ⊕ y.

x[ 4] ⊕= (x[ 0] ⊞ x[12])<<<7;    x[ 9] ⊕= (x[ 5] ⊞ x[ 1])<<<7;
x[14] ⊕= (x[10] ⊞ x[ 6])<<<7;    x[ 3] ⊕= (x[15] ⊞ x[11])<<<7;
x[ 8] ⊕= (x[ 4] ⊞ x[ 0])<<<9;    x[13] ⊕= (x[ 9] ⊞ x[ 5])<<<9;
x[ 2] ⊕= (x[14] ⊞ x[10])<<<9;    x[ 7] ⊕= (x[ 3] ⊞ x[15])<<<9;
x[12] ⊕= (x[ 8] ⊞ x[ 4])<<<13;   x[ 1] ⊕= (x[13] ⊞ x[ 9])<<<13;
x[ 6] ⊕= (x[ 2] ⊞ x[14])<<<13;   x[11] ⊕= (x[ 7] ⊞ x[ 3])<<<13;
x[ 0] ⊕= (x[12] ⊞ x[ 8])<<<18;   x[ 5] ⊕= (x[ 1] ⊞ x[13])<<<18;
x[10] ⊕= (x[ 6] ⊞ x[ 2])<<<18;   x[15] ⊕= (x[11] ⊞ x[ 7])<<<18;

x[ 1] ⊕= (x[ 0] ⊞ x[ 3])<<<7;    x[ 6] ⊕= (x[ 5] ⊞ x[ 4])<<<7;
x[11] ⊕= (x[10] ⊞ x[ 9])<<<7;    x[12] ⊕= (x[15] ⊞ x[14])<<<7;
x[ 2] ⊕= (x[ 1] ⊞ x[ 0])<<<9;    x[ 7] ⊕= (x[ 6] ⊞ x[ 5])<<<9;
x[ 8] ⊕= (x[11] ⊞ x[10])<<<9;    x[13] ⊕= (x[12] ⊞ x[15])<<<9;
x[ 3] ⊕= (x[ 2] ⊞ x[ 1])<<<13;   x[ 4] ⊕= (x[ 7] ⊞ x[ 6])<<<13;
x[ 9] ⊕= (x[ 8] ⊞ x[11])<<<13;   x[14] ⊕= (x[13] ⊞ x[12])<<<13;
x[ 0] ⊕= (x[ 3] ⊞ x[ 2])<<<18;   x[ 5] ⊕= (x[ 4] ⊞ x[ 7])<<<18;
x[10] ⊕= (x[ 9] ⊞ x[ 8])<<<18;   x[15] ⊕= (x[14] ⊞ x[13])<<<18;

Salsa20 performs 20 rounds of mixing on its input, then adds the final array to the original array to obtain its 64-byte output block.^[5] 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.

eSTREAM selection

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.^[6] 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,^[7] 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.^[8]

Cryptanalysis

As of 2012, there are no published attacks on Salsa20/12 or the full Salsa20/20; the best attack known^[2] 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".^[9] 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.^[10]

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.^[11] However, this attack does not seem to be comparative 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.^[2]

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.^[12]

In 2013, Mouha and Preneel published a proof^[13] 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.^[14] 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.^[2]

ChaCha replaces the basic Salsa20 round primitive R(a,b,c,k)

b ⊕= (a ⊞ c) <<< k;

with the modified computation:

b ⊞= c;
a ⊕= b;
a <<<= k;

The rotation amounts are also updated. A full quarter-round, QR (a,b,c,d) becomes:

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

In addition to being more efficient on 2-operand instruction sets (like x86), this updates each word twice per quarter-round.

The fact that two of the rotates are multiple of 8 allows some optimization.^[15] Additionally, the input formatting is 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.^[16] So a double round in ChaCha is

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

where the numbers are the indexes of the sixteen 32-bit state words. ChaCha20 uses 10 iterations of the double round.^[17]

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 OpenSSL, which is used for Internet security.^[18] Google's initial implementation is securing https (TLS/SSL) traffic between the Chrome browser on Android phones and Google's websites.^[19]

Shortly after Google's adoption for TLS, both ChaCha20 and Poly1305 algorithms have also been used for a new chacha20-poly1305@openssh.com cipher in OpenSSH.^[20][21] Subsequently, this made it possible for OpenSSH to not depend on OpenSSL through a compile-time option.^[22]

ChaCha20 is also used for random number generator arc4random in OpenBSD^[23] and NetBSD^[24] operating systems, instead of "broken" RC4, and in DragonFly BSD^[25] for the CSPRNG subroutine of the kernel.^[26][27]

See also

• Speck, an add-rotate-xor cipher developed by NSA.

References

External links

• Salsa20 home page
• Specification (PDF)
• Salsa20/8 and Salsa20/12 (PDF)
• eStream page on Salsa20
• The ChaCha family of stream ciphers
• Salsa20 Usage & Deployment

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