# SHA-1

Short description: Cryptographic hash function
SHA-1
General
DesignersNational Security Agency
First published1993 (SHA-0),
1995 (SHA-1)
Series(SHA-0), SHA-1, SHA-2, SHA-3
CertificationFIPS PUB 180-4, CRYPTREC (Monitored)
Cipher detail
Digest sizes160 bits
Block sizes512 bits
StructureMerkle–Damgård construction
Rounds80

In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographically broken[1][2][3][4][5][6][7] but still widely used hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecimal digits. It was designed by the United States National Security Agency, and is a U.S. Federal Information Processing Standard.[8]

Since 2005, SHA-1 has not been considered secure against well-funded opponents;[9] as of 2010 many organizations have recommended its replacement.[10][7][11] NIST formally deprecated use of SHA-1 in 2011 and disallowed its use for digital signatures in 2013. (As of 2020), chosen-prefix attacks against SHA-1 are practical.[3][5] As such, it is recommended to remove SHA-1 from products as soon as possible and instead use SHA-2 or SHA-3. Replacing SHA-1 is urgent where it is used for digital signatures.

All major web browser vendors ceased acceptance of SHA-1 SSL certificates in 2017.[12][6][1] In February 2017, CWI Amsterdam and Google announced they had performed a collision attack against SHA-1, publishing two dissimilar PDF files which produced the same SHA-1 hash.[13][14] However, SHA-1 is still secure for HMAC.[15]

Microsoft has discontinued SHA-1 code signing support for Windows Update on August 7, 2020.

## Development

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;
• $\displaystyle{ \lll_n }$ denotes a left bit rotation by n places;
• n varies for each operation;
• Wt is the expanded message word of round t;
• Kt is the round constant of round t;

SHA-1 produces a message digest based on principles similar to those used by Ronald L. Rivest of MIT in the design of the MD2, MD4 and MD5 message digest algorithms, but generates a larger hash value (160 bits vs. 128 bits).

SHA-1 was developed as part of the U.S. Government's Capstone project.[16] The original specification of the algorithm was published in 1993 under the title Secure Hash Standard, FIPS PUB 180, by U.S. government standards agency NIST (National Institute of Standards and Technology).[17][18] This version is now often named SHA-0. It was withdrawn by the NSA shortly after publication and was superseded by the revised version, published in 1995 in FIPS PUB 180-1 and commonly designated SHA-1. SHA-1 differs from SHA-0 only by a single bitwise rotation in the message schedule of its compression function. According to the NSA, this was done to correct a flaw in the original algorithm which reduced its cryptographic security, but they did not provide any further explanation.[19][20] Publicly available techniques did indeed demonstrate a compromise of SHA-0, in 2004, before SHA-1 in 2017 (see §Attacks).

## Applications

### Cryptography

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 and SHA-2 are the 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),[21] though that was later relaxed to allow SHA-1 to be used for verifying old digital signatures and time stamps.[22]

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 for the basis of the SHACAL block ciphers.

### Data integrity

Revision control systems such as Git, Mercurial, and Monotone use SHA-1, not for security, but to identify revisions and to ensure that the data has not changed due to accidental corruption. Linus Torvalds said about Git:

If you have disk corruption, if you have DRAM corruption, if you have any kind of problems at all, Git will notice them. It's not a question of if, it's a guarantee. You can have people who try to be malicious. They won't succeed. [...] Nobody has been able to break SHA-1, but the point is the SHA-1, as far as Git is concerned, isn't even a security feature. It's purely a consistency check. The security parts are elsewhere, so a lot of people assume that since Git uses SHA-1 and SHA-1 is used for cryptographically secure stuff, they think that, Okay, it's a huge security feature. It has nothing at all to do with security, it's just the best hash you can get. ...
I guarantee you, if you put your data in Git, you can trust the fact that five years later, after it was converted from your hard disk to DVD to whatever new technology and you copied it along, five years later you can verify that the data you get back out is the exact same data you put in. [...]
One of the reasons I care is for the kernel, we had a break in on one of the BitKeeper sites where people tried to corrupt the kernel source code repositories.[23]

However Git does not require the second preimage resistance of SHA-1 as a security feature, since it will always prefer to keep the earliest version of an object in case of collision, preventing an attacker from surreptitiously overwriting files.[24]

## 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 2L evaluations. This is called a preimage attack and may or may not be practical depending on L and the particular computing environment. However, a collision, consisting of finding two different messages that produce the same message digest, requires on average only about 1.2 × 2L/2 evaluations using a birthday attack. Thus the strength of a hash function is usually compared to a symmetric cipher of half the message digest length. SHA-1, which has a 160-bit message digest, was originally thought to have 80-bit strength.

Some of the applications that use cryptographic hashes, like 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.[25]

Due to the block and iterative structure of the algorithms and the absence of additional final steps, all SHA functions (except SHA-3[26]) are vulnerable to length-extension and partial-message collision attacks.[27] 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. A simple improvement to prevent these attacks is to hash twice: SHAd(message) = SHA(SHA(0b || message)) (the length of 0b, zero block, is equal to the block size of the hash function).

### SHA-0

At CRYPTO 98, two French researchers, Florent Chabaud and Antoine Joux, presented an attack on SHA-0: collisions can be found with complexity 261, fewer than the 280 for an ideal hash function of the same size.[28]

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.[29]

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 processor-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.[30][31]

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.[2][32]

Another attack in 2008 applying the boomerang attack brought the complexity of finding collisions down to 233.6, which was estimated to take 1 hour on an average PC from the year 2008.[33]

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.[34]

### Attacks

In early 2005, Vincent Rijmen and Elisabeth 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.[35]

In February 2005, an attack by Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced.[2] 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, 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."[36] 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."[37]

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.[4] On 18 December 2007 the details of this result were explained and verified by Martin Cochran.[38]

Christophe De Cannière and Christian Rechberger further improved the attack on SHA-1 in "Finding SHA-1 Characteristics: General Results and Applications,"[39] 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. Since this attack requires the equivalent of about 235 evaluations, it is considered to be a significant theoretical break.[40] Their attack was extended further to 73 rounds (of 80) in 2010 by Grechnikov.[41] In order to find an actual collision in the full 80 rounds of the hash function, however, tremendous 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.[42]

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.[43][44]

In 2008, an attack methodology by Stéphane Manuel reported hash collisions with an estimated theoretical complexity of 251 to 257 operations.[45] However he later retracted that claim after finding that local collision paths were not actually independent, and finally quoting for the most efficient a collision vector that was already known before this work.[46]

Cameron McDonald, Philip Hawkes and Josef Pieprzyk presented a hash collision attack with claimed complexity 252 at the Rump Session of Eurocrypt 2009.[47] 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.[48]

The authors estimated that the cost of renting enough of EC2 CPU/GPU time to generate a full collision for SHA-1 at the time of publication was between US$75K and 120K, and noted that was well within the budget of criminal organizations, not to mention national intelligence agencies. As such, the authors recommended that SHA-1 be deprecated as quickly as possible.[7] #### SHAttered – first public collision On 23 February 2017, the CWI (Centrum Wiskunde & Informatica) and Google announced the SHAttered attack, in which they generated two different PDF files with the same SHA-1 hash in roughly 263.1 SHA-1 evaluations. This attack is about 100,000 times faster than brute forcing a SHA-1 collision with a birthday attack, which was estimated to take 280 SHA-1 evaluations. The attack required "the equivalent processing power of 6,500 years of single-CPU computations and 110 years of single-GPU computations".[14] #### Birthday-Near-Collision Attack – first practical chosen-prefix attack On 24 April 2019 a paper by Gaëtan Leurent and Thomas Peyrin presented at Eurocrypt 2019 described an enhancement to the previously best chosen-prefix attack in Merkle–Damgård–like digest functions based on Davies–Meyer block ciphers. With these improvements, this method is capable of finding chosen-prefix collisions in approximately 268 SHA-1 evaluations. This is approximately 1 billion times faster (and now usable for many targeted attacks, thanks to the possibility of choosing a prefix, for example malicious code or faked identities in signed certificates) than the previous attack's 277.1 evaluations (but without chosen prefix, which was impractical for most targeted attacks because the found collisions were almost random)[52] and is fast enough to be practical for resourceful attackers, requiring approximately$100,000 of cloud processing. This method is also capable of finding chosen-prefix collisions in the MD5 function, but at a complexity of 246.3 does not surpass the prior best available method at a theoretical level (239), though potentially at a practical level (≤249).[53][54] This attack has a memory requirement of 500+ GB.

On 5 January 2020 the authors published an improved attack.[5] In this paper they demonstrate a chosen-prefix collision attack with a complexity of 263.4, that at the time of publication would cost 45k USD per generated collision.

### Official validation

Main page: 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 the formal CMVP validation, which is required by law for certain applications.

(As of 2013), there are over 2000 validated implementations of SHA-1, with 14 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 hexadecimal and in Base64 binary to ASCII text encoding.

• SHA1("The quick brown fox jumps over the lazy dog")
• Outputted hexadecimal: 2fd4e1c67a2d28fced849ee1bb76e7391b93eb12
• Outputted Base64 binary to ASCII text encoding: L9ThxnotKPzthJ7hu3bnORuT6xI=

Even a small change in the message will, with overwhelming probability, result in many bits changing 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")
• Outputted hexadecimal: de9f2c7fd25e1b3afad3e85a0bd17d9b100db4b3
• Outputted Base64 binary to ASCII text encoding: 3p8sf9JeGzr60+haC9F9mxANtLM=

The hash of the zero-length string is:

• SHA1("")
• Outputted hexadecimal: da39a3ee5e6b4b0d3255bfef95601890afd80709
• Outputted 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-bit quantities and wrap modulo 232 when calculating, except for
ml, the message length, which is a 64-bit quantity, and
hh, the message digest, which is a 160-bit quantity.
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
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 e.g. by adding 0x80 if message length is a multiple of 8 bits.
append 0 ≤ k < 512 bits '0', such that the resulting message length in bits
is congruent to −64 ≡ 448 (mod 512)
append ml, the original message length in bits, as a 64-bit big-endian integer.
Thus, the total 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

Message schedule: extend the sixteen 32-bit words into eighty 32-bit words:
for i from 16 to 79
Note 3: SHA-0 differs by not having this leftrotate.
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:[8][55]
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 in hexadecimal (base 16).

The chosen constant values used in the algorithm were assumed to be nothing up my sleeve numbers:

• The four round constants k are 230 times the square roots of 2, 3, 5 and 10. However they were incorrectly rounded to the nearest integer instead of being rounded to the nearest odd integer, with equilibrated proportions of zero and one bits. As well, choosing the square root of 10 (which is not a prime) made it a common factor for the two other chosen square roots of primes 2 and 5, with possibly usable arithmetic properties across successive rounds, reducing the strength of the algorithm against finding collisions on some bits.
• The first four starting values for h0 through h3 are the same with the MD5 algorithm, and the fifth (for h4) is similar. However they were not properly verified for being resistant against inversion of the few first rounds to infer possible collisions on some bits, usable by multiblock differential attacks.

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:

Bitwise choice between c and d, controlled by b.
(0  ≤ i ≤ 19): f = d xor (b and (c xor d))                (alternative 1)
(0  ≤ i ≤ 19): f = (b and c) or ((not b) and d)           (alternative 2)
(0  ≤ i ≤ 19): f = (b and c) xor ((not b) and d)          (alternative 3)
(0  ≤ i ≤ 19): f = vec_sel(d, c, b)                       (alternative 4)
[premo08]
Bitwise majority function.
(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) xor (d and (b xor c))        (alternative 3)
(40 ≤ i ≤ 59): f = (b and c) xor (b and d) xor (c and d)  (alternative 4)
(40 ≤ i ≤ 59): f = vec_sel(c, b, c xor d)                 (alternative 5)


It was also shown[56] 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 like x86 SSE instructions.

## Comparison of SHA functions

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

Comparison of SHA functions
Algorithm and variant Output size
(bits)
Internal state size
(bits)
Block size
(bits)
Rounds Operations Security (in bits) against collision attacks Capacity
against length extension attacks
Performance on Skylake (median cpb)[57] First published
long messages 8 bytes
MD5 (as reference) 128 128
(4 × 32)
512 64 And, Xor, Rot, Add (mod 232), Or ≤18
(collisions found)[58]
0 4.99 55.00 1992
SHA-0 160 160
(5 × 32)
512 80 And, Xor, Rot, Add (mod 232), Or <34
(collisions found)
0 ≈ SHA-1 ≈ SHA-1 1993
SHA-1 <63
(collisions found)[59]
3.47 52.00 1995
SHA-2 SHA-224
SHA-256
224
256
256
(8 × 32)
512 64 And, Xor, Rot, Add (mod 232), Or, Shr 112
128
32
0
7.62
7.63
84.50
85.25
2004
2001
SHA-384
SHA-512
384
512
512
(8 × 64)
1024 80 And, Xor, Rot, Add (mod 264), Or, Shr 192
256
128 (≤ 384)
0
5.12
5.06
135.75
135.50
2001
SHA-512/224
SHA-512/256
224
256
112
128
288
256
≈ SHA-384 ≈ SHA-384 2012
SHA-3 SHA3-224
SHA3-256
SHA3-384
SHA3-512
224
256
384
512
1600
(5 × 5 × 64)
1152
1088
832
576
24[60] And, Xor, Rot, Not 112
128
192
256
448
512
768
1024
8.12
8.59
11.06
15.88
154.25
155.50
164.00
164.00
2015
SHAKE128
SHAKE256
d (arbitrary)
d (arbitrary)
1344
1088
min(d/2, 128)
min(d/2, 256)
256
512
7.08
8.59
155.25
155.50

## Implementations

Below is a list of cryptography libraries that support SHA-1:

Hardware acceleration is provided by the following processor extensions:

• Intel SHA extensions: Available on some Intel and AMD x86 processors.
• IBM z/Architecture: Available since 2003 as part of the Message-Security-Assist Extension[61]

## Notes

1. Gaëtan Leurent; Thomas Peyrin (2020-01-05). "SHA-1 is a Shambles First Chosen-Prefix Collision on SHA-1 and Application to the PGP Web of Trust". Cryptology ePrint Archive, Report 2020/014.
2. Stevens1, Marc; Karpman, Pierre; Peyrin, Thomas. "The SHAppening: freestart collisions for SHA-1".
3. Schneier, Bruce (February 18, 2005). "Schneier on Security: Cryptanalysis of SHA-1".
4. Schneier, Bruce (8 October 2015). "SHA-1 Freestart Collision". Schneier on Security.
5. Cite error: Invalid <ref> tag; no text was provided for refs named sha1-shattered
6. Barker, Elaine (May 2020). "Recommendation for Key Management: Part 1 – General, Table 3.". NIST, Technical Report: 56. doi:10.6028/NIST.SP.800-57pt1r5.
7. Selvarani, R.; Aswatha, Kumar; T V Suresh, Kumar (2012). Proceedings of International Conference on Advances in Computing. Springer Science & Business Media. p. 551. ISBN 978-81-322-0740-5.
8. Secure Hash Standard, Federal Information Processing Standards Publication FIPS PUB 180, 11 May 1993
9. National Institute on Standards and Technology Computer Security Resource Center, NIST's March 2006 Policy on Hash Functions , accessed September 28, 2012.
10. National Institute on Standards and Technology Computer Security Resource Center, NIST's Policy on Hash Functions , accessed September 28, 2012.
11. Sotirov, Alexander; Stevens, Marc; Appelbaum, Jacob; Lenstra, Arjen; Molnar, David; Osvik, Dag Arne; de Weger, Benne (December 30, 2008). "MD5 considered harmful today: Creating a rogue CA certificate".
12. "Strengths of Keccak – Design and security". Keccak team. "Unlike SHA-1 and SHA-2, Keccak does not have the length-extension weakness, hence does not need the HMAC nested construction. Instead, MAC computation can be performed by simply prepending the message with the key."
13. Niels Ferguson, Bruce Schneier, and Tadayoshi Kohno, Cryptography Engineering, John Wiley & Sons, 2010. ISBN:978-0-470-47424-2
14. Chabaud, Florent; Joux, Antoine (1998). "Differential collisions in SHA-0". in Krawczyk, Hugo. Advances in Cryptology – CRYPTO 1998. Lecture Notes in Computer Science. 1462. Springer. pp. 56–71. doi:10.1007/bfb0055720. ISBN 9783540648925.
15.
16. Grieu, Francois (18 August 2004). "Re: Any advance news from the crypto rump session?". Newsgroupsci.crypt. Event occurs at 05:06:02 +0200. Usenet: fgrieu-05A994.05060218082004@individual.net.
17. Efficient Collision Search Attacks on SHA-0 , Shandong University
18. Manuel, Stéphane; Peyrin, Thomas (2008-02-11). "Collisions on SHA-0 in One Hour". Fast Software Encryption 2008. 5086. pp. 16–35. doi:10.1007/978-3-540-71039-4_2. ISBN 978-3-540-71038-7.
19. Rijmen, Vincent; Oswald, Elisabeth (2005). Update on SHA-1.
20. Lemos, Robert. "Fixing a hole in security". ZDNet.
21. Cochran, Martin (2007). "Notes on the Wang et al. 263 SHA-1 Differential Path".
22. De Cannière, Christophe; Rechberger, Christian (2006-11-15). "Finding SHA-1 Characteristics: General Results and Applications". Advances in Cryptology – ASIACRYPT 2006. Lecture Notes in Computer Science. 4284. pp. 1–20. doi:10.1007/11935230_1. ISBN 978-3-540-49475-1.
23. Manuel, Stéphane (2011). "Classification and Generation of Disturbance Vectors for Collision Attacks against SHA-1". Designs, Codes and Cryptography 59 (1–3): 247–263. doi:10.1007/s10623-010-9458-9.  the most efficient disturbance vector is Codeword2 first reported by Jutla and Patthak
24. McDonald, Cameron; Hawkes, Philip; Pieprzyk, Josef (2009). Differential Path for SHA-1 with complexity O(252).  (withdrawn)
25. Leurent, Gaëtan; Peyrin, Thomas (2019). "From Collisions to Chosen-Prefix Collisions Application to Full SHA-1". Advances in Cryptology – EUROCRYPT 2019. Lecture Notes in Computer Science. 11478. pp. 527–555. doi:10.1007/978-3-030-17659-4_18. ISBN 978-3-030-17658-7.
26. Gaëtan Leurent; Thomas Peyrin (2019-04-24). "From Collisions to Chosen-Prefix Collisions - Application to Full SHA-1". Eurocrypt 2019.
27. Locktyukhin, Max (2010-03-31), "Improving the Performance of the Secure Hash Algorithm (SHA-1)", Intel Software Knowledge Base, retrieved 2010-04-02
28. Tao, Xie; Liu, Fanbao; Feng, Dengguo (2013). Fast Collision Attack on MD5 (PDF). Cryptology ePrint Archive (Technical report). IACR.
29. Stevens, Marc; Bursztein, Elie; Karpman, Pierre; Albertini, Ange; Markov, Yarik. The first collision for full SHA-1 (PDF) (Technical report). Google Research. Lay summaryGoogle Security Blog (February 23, 2017).
30. "The Keccak sponge function family". Retrieved 2016-01-27.
31. IBM z/Architecture Principles of Operation, publication number SA22-7832. See KIMD and KLMD instructions in Chapter 7.