SHA-1

SHA-1

General
Designers	National Security Agency
First published	1993 (SHA-0), 1995 (SHA-1)
Series	(SHA-0), SHA-1, SHA-2, SHA-3
Certification	FIPS PUB 180-4, CRYPTREC (Monitored)
Detail
Digest sizes	160 bits
Structure	Merkle–Damgård construction
Rounds	80
Best public cryptanalysis
A 2011 attack by Marc Stevens can produce hash collisions with a complexity of 261 operations. No actual collisions have yet been produced.

In cryptography, SHA-1 is a cryptographic hash function designed by the United States National Security Agency and published by the United States NIST as a U.S. Federal Information Processing Standard.

SHA-1 produces a 160-bit (20-byte) hash value. A SHA-1 hash value is typically expressed as a hexadecimal number, 40 digits long.

SHA stands for "secure hash algorithm". The four SHA algorithms are structured differently and are distinguished as SHA-0, SHA-1, SHA-2, and SHA-3. SHA-1 is very similar to SHA-0, but corrects an error in the original SHA hash specification that led to significant weaknesses. The SHA-0 algorithm was not adopted by many applications. SHA-2 on the other hand significantly differs from the SHA-1 hash function.

SHA-1 is the most widely used of the existing SHA hash functions, and is employed in several widely used applications and protocols.

In 2005, cryptanalysts found attacks on SHA-1 suggesting that the algorithm might not be secure enough for ongoing use. NIST required many applications in federal agencies to move to SHA-2 after 2010 because of the weakness. Although no successful attacks have yet been reported on SHA-2, they are algorithmically similar to SHA-1. In 2012, following a long-running competition, NIST selected an additional algorithm, Keccak, for standardization as SHA-3. In 2013 Microsoft announced their deprecation policy on SHA1 according to which Windows will stop accepting SHA1 certificates in SSL by 2017

The SHA-1 hash function

One iteration within the SHA-1 compression function:
A, B, C, D and E are 32-bit words of the state;
F is a nonlinear function that varies;
_n denotes a left bit rotation by n places;
n varies for each operation;
W_t is the expanded message word of round t;
K_t is the round constant of round t;
denotes addition modulo 2³².

SHA-1 produces a message digest based on principles similar to those used by Ronald L. Rivest of MIT in the design of the MD4 and MD5 message digest algorithms, but has a more conservative design.

The original specification of the algorithm was published in 1993 as the Secure Hash Standard, FIPS PUB 180, by U.S. government standards agency NIST (National Institute of Standards and Technology). This version is now often referred to as SHA-0. It was withdrawn by NSA shortly after publication and was superseded by the revised version, published in 1995 in FIPS PUB 180-1 and commonly referred to as SHA-1. SHA-1 differs from SHA-0 only by a single bitwise rotation in the message schedule of its compression function; this was done, according to NSA, to correct a flaw in the original algorithm which reduced its cryptographic security. However, NSA did not provide any further explanation or identify the flaw that was corrected. Weaknesses have subsequently been reported in both SHA-0 and SHA-1. SHA-1 appears to provide greater resistance to attacks , supporting the NSA’s assertion that the change increased the security.

Comparison of SHA functions

In the table below, internal state means the “internal hash sum” after each compression of a data block.

Further information: Merkle–Damgård construction

Algorithm and variant		Output size (bits)	Internal state size (bits)	Block size (bits)	Max message size (bits)	Word size (bits)	Rounds	Operations	Collisions found?
SHA-0		160	160	512	264 − 1	32	80	add, and, or, xor, rotate, mod	Yes
SHA-1									Theoretical attack (260)
SHA-2	SHA-256/224	256/224	256	512	264 − 1	32	64	add, and, or, xor, rotate, mod, shift	No
	SHA-512/384	512/384	512	1024	2128 − 1	64	80

Applications

Cryptography

Further information: Cryptographic hash function § Applications

SHA-1 forms part of several widely used security applications and protocols, including TLS and SSL, PGP, SSH, S/MIME, and IPsec. Those applications can also use MD5; both MD5 and SHA-1 are descended from MD4. SHA-1 hashing is also used in distributed revision control systems such as Git, Mercurial, and Monotone to identify revisions, and to detect data corruption or tampering. The algorithm has also been used on Nintendo's Wii gaming console for signature verification when booting, but a significant implementation flaw allows for an attacker to bypass the system's security scheme.

SHA-1 and SHA-2 are the secure hash algorithms required by law for use in certain U.S. Government applications, including use within other cryptographic algorithms and protocols, for the protection of sensitive unclassified information. FIPS PUB 180-1 also encouraged adoption and use of SHA-1 by private and commercial organizations. SHA-1 is being retired from most government uses; the U.S. National Institute of Standards and Technology said, "Federal agencies should stop using SHA-1 for...applications that require collision resistance as soon as practical, and must use the SHA-2 family of hash functions for these applications after 2010" (emphasis in original), though that was later relaxed.

A prime motivation for the publication of the Secure Hash Algorithm was the Digital Signature Standard, in which it is incorporated.

The SHA hash functions have been used as the basis for the SHACAL block ciphers.

Data integrity

The source control management system Git uses SHA-1 not for security but for ensuring that the data has not changed. Linus Torvalds has said, "Git uses SHA-1 in a way which has nothing at all to do with security.... It's just the best hash you can get.... It's about the ability to trust your data. I guarantee you, if you put your data in Git, you can trust the fact that five years later, after it was converted from a hard disk to a DVD to whatever new technology and you copied it, five years later you can verify that the data that you get back out is the exact same data you put in."

Cryptanalysis and validation

For a hash function for which L is the number of bits in the message digest, finding a message that corresponds to a given message digest can always be done using a brute force search in approximately 2^L evaluations. This is called a preimage attack and may or may not be practical depending on L and the particular computing environment. The second criterion, finding two different messages that produce the same message digest, known as a collision, requires on average only about 1.2 * 2^{L / 2} evaluations using a birthday attack. For the latter reason the strength of a hash function is usually compared to a symmetric cipher of half the message digest length. Thus SHA-1 was originally thought to have 80-bit strength.

Cryptographers have produced collision pairs for SHA-0 and have found algorithms that should produce SHA-1 collisions in far fewer than the originally expected 2⁸⁰ evaluations.

In terms of practical security, a major concern about these new attacks is that they might pave the way to more efficient ones. Whether this is the case is yet to be seen, but a migration to stronger hashes is believed to be prudent. Some of the applications that use cryptographic hashes, such as password storage, are only minimally affected by a collision attack. Constructing a password that works for a given account requires a preimage attack, as well as access to the hash of the original password, which may or may not be trivial. Reversing password encryption (e.g. to obtain a password to try against a user's account elsewhere) is not made possible by the attacks. (However, even a secure password hash can't prevent brute-force attacks on weak passwords.)

In the case of document signing, an attacker could not simply fake a signature from an existing document—the attacker would have to produce a pair of documents, one innocuous and one damaging, and get the private key holder to sign the innocuous document. There are practical circumstances in which this is possible; until the end of 2008, it was possible to create forged SSL certificates using an MD5 collision.

Due to the block and iterative structure of the algorithms and the absence of additional final steps, all SHA functions are vulnerable to length-extension and partial-message collision attacks. These attacks allow an attacker to forge a message signed only by a keyed hash – $SHA(message||key)$ or $SHA(key||message)$ – by extending the message and recalculating the hash without knowing the key. The simplest improvement to prevent these attacks is to hash twice: $SHA_{d}(message)=SHA(SHA(0^{b}||message))$ (the length of $0^{b}$, zero block, is equal to the block size of hash function).

Attacks

In early 2005, Rijmen and Oswald published an attack on a reduced version of SHA-1—53 out of 80 rounds—which finds collisions with a computational effort of fewer than 2⁸⁰ operations.

In February 2005, an attack by Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced. The attacks can find collisions in the full version of SHA-1, requiring fewer than 2⁶⁹ operations. (A brute-force search would require 2⁸⁰ operations.)

The authors write: "In particular, our analysis is built upon the original differential attack on SHA-0 [sic], the near collision attack on SHA-0, the multiblock collision techniques, as well as the message modification techniques used in the collision search attack on MD5. Breaking SHA-1 would not be possible without these powerful analytical techniques." The authors have presented a collision for 58-round SHA-1, found with 2³³ hash operations. The paper with the full attack description was published in August 2005 at the CRYPTO conference.

In an interview, Yin states that, "Roughly, we exploit the following two weaknesses: One is that the file preprocessing step is not complicated enough; another is that certain math operations in the first 20 rounds have unexpected security problems."

On 17 August 2005, an improvement on the SHA-1 attack was announced on behalf of Xiaoyun Wang, Andrew Yao and Frances Yao at the CRYPTO 2005 rump session, lowering the complexity required for finding a collision in SHA-1 to 2⁶³. On 18 December 2007 the details of this result were explained and verified by Martin Cochran.

Christophe De Cannière and Christian Rechberger further improved the attack on SHA-1 in "Finding SHA-1 Characteristics: General Results and Applications," receiving the Best Paper Award at ASIACRYPT 2006. A two-block collision for 64-round SHA-1 was presented, found using unoptimized methods with 2³⁵ compression function evaluations. As this attack requires the equivalent of about 2³⁵ evaluations, it is considered to be a significant theoretical break. Their attack was extended further to 73 rounds (of 80) in 2010 by Grechnikov. In order to find an actual collision in the full 80 rounds of the hash function, however, massive amounts of computer time are required. To that end, a collision search for SHA-1 using the distributed computing platform BOINC began August 8, 2007, organized by the Graz University of Technology. The effort was abandoned May 12, 2009 due to lack of progress.

At the Rump Session of CRYPTO 2006, Christian Rechberger and Christophe De Cannière claimed to have discovered a collision attack on SHA-1 that would allow an attacker to select at least parts of the message.

In 2008, an attack methodology by Stéphane Manuel reported hash collisions with an estimated theoretical complexity of 2⁵¹ to 2⁵⁷ operations. However he later retracted that claim after finding that local collision paths were not actually independent, and finally quoting as the most efficient a collision vector that was already known before this work.

Cameron McDonald, Philip Hawkes and Josef Pieprzyk presented a hash collision attack with claimed complexity 2⁵² at the Rump session of Eurocrypt 2009. However, the accompanying paper, "Differential Path for SHA-1 with complexity O(2⁵²)" has been withdrawn due to the authors' discovery that their estimate was incorrect.

As of 2012, the most efficient attack against SHA-1 is considered to be the one by Marc Stevens with an estimated cost of $2.77M to break a single hash value by renting CPU power from cloud servers. Stevens developed this attack in a project called HashClash, implementing a differential path attack. On 8 November 2010, he claimed he had a fully working near-collision attack against full SHA-1 working with an estimated complexity equivalent to 2^57.5 SHA-1 compressions. He estimates this attack can be extended to a full collision with a complexity around 2⁶¹.

SHA-0

At CRYPTO 98, two French researchers, Florent Chabaud and Antoine Joux, presented an attack on SHA-0 (Chabaud and Joux, 1998): collisions can be found with complexity 2⁶¹, fewer than the 2⁸⁰ for an ideal hash function of the same size.

In 2004, Biham and Chen found near-collisions for SHA-0—two messages that hash to nearly the same value; in this case, 142 out of the 160 bits are equal. They also found full collisions of SHA-0 reduced to 62 out of its 80 rounds.

Subsequently, on 12 August 2004, a collision for the full SHA-0 algorithm was announced by Joux, Carribault, Lemuet, and Jalby. This was done by using a generalization of the Chabaud and Joux attack. Finding the collision had complexity 2⁵¹ and took about 80,000 CPU hours on a supercomputer with 256 Itanium 2 processors. (Equivalent to 13 days of full-time use of the computer.)

On 17 August 2004, at the Rump Session of CRYPTO 2004, preliminary results were announced by Wang, Feng, Lai, and Yu, about an attack on MD5, SHA-0 and other hash functions. The complexity of their attack on SHA-0 is 2⁴⁰, significantly better than the attack by Joux et al.

In February 2005, an attack by Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced which could find collisions in SHA-0 in 2³⁹ operations.

In light of the results for SHA-0, some experts suggested that plans for the use of SHA-1 in new cryptosystems should be reconsidered. After the CRYPTO 2004 results were published, NIST announced that they planned to phase out the use of SHA-1 by 2010 in favor of the SHA-2 variants.

Official validation

Main article: Cryptographic Module Validation Program

Implementations of all FIPS-approved security functions can be officially validated through the CMVP program, jointly run by the National Institute of Standards and Technology (NIST) and the Communications Security Establishment (CSE). For informal verification, a package to generate a high number of test vectors is made available for download on the NIST site; the resulting verification however does not replace, in any way, the formal CMVP validation, which is required by law for certain applications.

As of February 2011, there are nearly 1400 validated implementations of SHA-1, with around a dozen of them capable of handling messages with a length in bits not a multiple of eight (see SHS Validation List).

Examples and pseudocode

Example hashes

These are examples of SHA-1 message digests in hexidecimal and in Base64 binary to ASCII text encoding.

SHA1("The quick brown fox jumps over the lazy dog")
gives hexidecimal: 2fd4e1c6 7a2d28fc ed849ee1 bb76e739 1b93eb12
gives Base64 binary to ASCII text encoding: L9ThxnotKPzthJ7hu3bnORuT6xI=

Even a small change in the message will, with overwhelming probability, result in a completely different hash due to the avalanche effect. For example, changing dog to cog produces a hash with different values for 81 of the 160 bits:

SHA1("The quick brown fox jumps over the lazy cog")
gives hexidecimal: de9f2c7f d25e1b3a fad3e85a 0bd17d9b 100db4b3
gives Base64 binary to ASCII text encoding: 3p8sf9JeGzr60+haC9F9mxANtLM=

The hash of the zero-length string is:

SHA1("")
gives hexidecimal: da39a3ee 5e6b4b0d 3255bfef 95601890 afd80709
gives Base64 binary to ASCII text encoding: 2jmj7l5rSw0yVb/vlWAYkK/YBwk=

SHA-1 pseudocode

Pseudocode for the SHA-1 algorithm follows:

Note 1: All variables are unsigned 32 bits and wrap modulo 232 when calculating, except
        ml the message length which is 64 bits, and
        hh the message digest which is 160 bits.
Note 2: All constants in this pseudo code are in big endian.
        Within each word, the most significant byte is stored in the leftmost byte position

Initialize variables:

h0 = 0x67452301
h1 = 0xEFCDAB89
h2 = 0x98BADCFE
h3 = 0x10325476
h4 = 0xC3D2E1F0

ml = message length in bits (always a multiple of the number of bits in a character).

Pre-processing:
append the bit '1' to the message i.e. by adding 0x80 if characters are 8 bits. 
append 0 ≤ k < 512 bits '0', so that the resulting message length (in bits)
   is congruent to 448 (mod 512)
append ml, as a 64-bit big-endian integer. So now the message length is a multiple of 512 bits.

Process the message in successive 512-bit chunks:
break message into 512-bit chunks
for each chunk
    break chunk into sixteen 32-bit big-endian words w[i], 0 ≤ i ≤ 15

    Extend the sixteen 32-bit words into eighty 32-bit words:
    for i from 16 to 79
        w[i] = (w[i-3] xor w[i-8] xor w[i-14] xor w[i-16]) leftrotate 1

    Initialize hash value for this chunk:
    a = h0
    b = h1
    c = h2
    d = h3
    e = h4

    Main loop:
    for i from 0 to 79
        if 0 ≤ i ≤ 19 then
            f = (b and c) or ((not b) and d)
            k = 0x5A827999
        else if 20 ≤ i ≤ 39
            f = b xor c xor d
            k = 0x6ED9EBA1
        else if 40 ≤ i ≤ 59
            f = (b and c) or (b and d) or (c and d) 
            k = 0x8F1BBCDC
        else if 60 ≤ i ≤ 79
            f = b xor c xor d
            k = 0xCA62C1D6

        temp = (a leftrotate 5) + f + e + k + w[i]
        e = d
        d = c
        c = b leftrotate 30
        b = a
        a = temp

    Add this chunk's hash to result so far:
    h0 = h0 + a
    h1 = h1 + b 
    h2 = h2 + c
    h3 = h3 + d
    h4 = h4 + e

Produce the final hash value (big-endian) as a 160 bit number:
hh = (h0 leftshift 128) or (h1 leftshift 96) or (h2 leftshift 64) or (h3 leftshift 32) or h4

The number hh is the message digest, which can be written as hexedecimal (base 16), but is often written using Base64 binary to ASCII text encoding.

The constant values used are chosen as nothing up my sleeve numbers: the four round constants k are 2³⁰ times the square roots of 2, 3, 5 and 10. The first four starting values for h0 through h3 are the same as the MD5 algorithm, and the fifth (for h4) is similar.

Instead of the formulation from the original FIPS PUB 180-1 shown, the following equivalent expressions may be used to compute f in the main loop above:

(0  ≤ i ≤ 19): f = d xor (b and (c xor d))                (alternative 1)
(0  ≤ i ≤ 19): f = (b and c) xor ((not b) and d)          (alternative 2)
(0  ≤ i ≤ 19): f = (b and c) + ((not b) and d)            (alternative 3)
(0  ≤ i ≤ 19): f = vec_sel(d, c, b)                       (alternative 4)
 
(40 ≤ i ≤ 59): f = (b and c) or (d and (b or c))          (alternative 1)
(40 ≤ i ≤ 59): f = (b and c) or (d and (b xor c))         (alternative 2)
(40 ≤ i ≤ 59): f = (b and c) + (d and (b xor c))          (alternative 3)
(40 ≤ i ≤ 59): f = (b and c) xor (b and d) xor (c and d)  (alternative 4)

Max Locktyukhin has also shown that for the rounds 32–79 the computation of:

w[i] = (w[i-3] xor w[i-8] xor w[i-14] xor w[i-16]) leftrotate 1

can be replaced with:

w[i] = (w[i-6] xor w[i-16] xor w[i-28] xor w[i-32]) leftrotate 2

This transformation keeps all operands 64-bit aligned and, by removing the dependency of w[i] on w[i-3], allows efficient SIMD implementation with a vector length of 4 such as x86 SSE instructions.

See also

• Comparison of cryptographic hash functions
• cryptlib
• Crypto++
• Digital timestamping
• Hashcash
• Hash collision
• International Association for Cryptologic Research
• Libgcrypt
• md5deep
• OpenSSL
• PolarSSL
• RIPEMD-160
• Secure Hash Standard
• sha1sum
• Tiger (cryptography)
• Whirlpool (cryptography)

References

• Florent Chabaud, Antoine Joux: Differential Collisions in SHA-0. CRYPTO 1998. pp56–71
• Eli Biham, Rafi Chen, Near-Collisions of SHA-0, Cryptology ePrint Archive, Report 2004/146, 2004 (appeared on CRYPTO 2004), IACR.org
• Xiaoyun Wang, Hongbo Yu and Yiqun Lisa Yin, Efficient Collision Search Attacks on SHA-0, CRYPTO 2005, CMU.edu
• Xiaoyun Wang, Yiqun Lisa Yin and Hongbo Yu, Finding Collisions in the Full SHA-1, Crypto 2005 MIT.edu
• Henri Gilbert, Helena Handschuh: Security Analysis of SHA-256 and Sisters. Selected Areas in Cryptography 2003: pp175–193
• http://www.unixwiz.net/techtips/iguide-crypto-hashes.html
• "Proposed Revision of Federal Information Processing Standard (FIPS) 180, Secure Hash Standard". Federal Register. 59 (131): 35317–35318. 1994-07-11. Retrieved 2007-04-26. {{cite journal}}: Cite has empty unknown parameter: |coauthors= (help)
• A. Cilardo, L. Esposito, A. Veniero, A. Mazzeo, V. Beltran, E. Ayugadé, A CellBE-based HPC application for the analysis of vulnerabilities in cryptographic hash functions, High Performance Computing and Communication international conference, August 2010

External links

• CSRC Cryptographic Toolkit – Official NIST site for the Secure Hash Standard
• FIPS 180-4: Secure Hash Standard (SHS) (PDF, 1.7 MB) – Current version of the Secure Hash Standard (SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512), March 2012
• RFC 3174 (with sample C implementation)
• Interview with Yiqun Lisa Yin concerning the attack on SHA-1
• Lenstra's Summary of impact of the February 2005 cryptanalytic results
• Explanation of the successful attacks on SHA-1 (3 pages, 2006)
• Cryptography Research – Hash Collision Q&A
• Online SHA1 hash crack using Rainbow tables
• Hash Project Web Site: software- and hardware-based cryptanalysis of SHA-1
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