| Secure Hash Algorithms | |
|---|---|
| Concepts | |
| hash functions,SHA,DSA | |
| Main standards | |
| SHA-0,SHA-1,SHA-2,SHA-3 | |
| 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) |
| Cipher detail | |
| Digest sizes | 160 bits |
| Block sizes | 512 bits |
| Structure | Merkle–Damgård construction |
| Rounds | 80 |
| Best publiccryptanalysis | |
| A 2011 attack by Marc Stevens can produce hash collisions with a complexity between 260.3 and 265.3 operations.[1] The first public collision was published on 23 February 2017.[2] SHA-1 is prone tolength extension attacks. | |
Incryptography,SHA-1 (Secure Hash Algorithm 1) is ahash function which takes an input and produces a 160-bit (20-byte) hash value known as amessage digest – typically rendered as 40hexadecimal digits. It was designed by the United StatesNational Security Agency, and is a U.S.Federal Information Processing Standard.[3] The algorithm has been cryptographically broken[4][5][6][7][8][9][10] but is still widely used.
Since 2005, SHA-1 has not been considered secure against well-funded opponents;[11] as of 2010 many organizations have recommended its replacement.[12][10][13]NIST formally deprecated use of SHA-1 in 2011 and disallowed its use for digital signatures in 2013, and declared that it should be phased out by 2030.[14] As of 2020[update],chosen-prefix attacks against SHA-1 are practical.[6][8] As such, it is recommended to remove SHA-1 from products as soon as possible and instead useSHA-2 orSHA-3. Replacing SHA-1 is urgent where it is used fordigital signatures.
All majorweb browser vendors ceased acceptance of SHA-1SSL certificates in 2017.[15][9][4] In February 2017,CWI Amsterdam andGoogle announced they had performed acollision attack against SHA-1, publishing two dissimilar PDF files which produced the same SHA-1 hash.[16][2] However, SHA-1 is still secure forHMAC.[17]
Microsoft has discontinued SHA-1 code signing support forWindows Update on August 3, 2020,[18] which also effectively ended the update servers for versions ofWindows that have not been updated to SHA-2, such asWindows 2000 up toVista, as well asWindows Server versions fromWindows 2000 Server toServer 2003.
denotes addition modulo 232.SHA-1 produces amessage digest based on principles similar to those used byRonald L. Rivest ofMIT in the design of theMD2,MD4 andMD5 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'sCapstone project.[19] The original specification of the algorithm was published in 1993 under the titleSecure Hash Standard,FIPS PUB 180, by U.S. government standards agencyNIST (National Institute of Standards and Technology).[20][21] This version is now often namedSHA-0. It was withdrawn by theNSA shortly after publication and was superseded by the revised version, published in 1995 in FIPS PUB 180-1 and commonly designatedSHA-1. SHA-1 differs from SHA-0 only by a single bitwise rotation in the message schedule of itscompression 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.[22][23] Publicly available techniques did indeed demonstrate a compromise of SHA-0, in 2004, before SHA-1 in 2017 (see§Attacks).
SHA-1 forms part of several widely used security applications and protocols, includingTLS andSSL,PGP,SSH,S/MIME, andIPsec. Those applications can also useMD5; both MD5 and SHA-1 are descended fromMD4.
SHA-1 and SHA-2 are the hash algorithms required by law for use in certainU.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 theSHA-2 family of hash functions for these applications after 2010",[24] though that was later relaxed to allow SHA-1 to be used for verifying old digital signatures and time stamps.[24]
A prime motivation for the publication of theSecure Hash Algorithm was theDigital Signature Standard, in which it is incorporated.
The SHA hash functions have been used for the basis of theSHACALblock ciphers.
Revision control systems such asGit,Mercurial, andMonotone 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 in 2007:
However Git does not require thesecond 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.[26] The known attacks (as of 2020) also do not break second preimage resistance.[27]
For a hash function for whichL 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 apreimage attack and may or may not be practical depending onL and the particular computing environment. However, acollision, consisting of finding two different messages that produce the same message digest, requires on average only about1.2 × 2L/2 evaluations using abirthday attack. Thus thestrength 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 apreimage 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 onweak passwords.SeePassword cracking.
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 forgedSSL certificates using anMD5 collision.[28]
Due to the block and iterative structure of the algorithms and the absence of additional final steps, all SHA functions (except SHA-3)[29] are vulnerable tolength-extension and partial-message collision attacks.[30] These attacks allow an attacker to forge a message signed only by a keyed hash –SHA(key ||message), but notSHA(message ||key) – 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).
AtCRYPTO 98, two French researchers,Florent Chabaud andAntoine 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.[31]
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.[32]
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 asupercomputer with 256Itanium 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 byWang, Feng, Lai, and Yu, about an attack onMD5, SHA-0 and other hash functions. The complexity of their attack on SHA-0 is 240, significantly better than the attack by Jouxet al.[33][34]
In February 2005, an attack byXiaoyun Wang,Yiqun Lisa Yin, and Hongbo Yu was announced which could find collisions in SHA-0 in 239 operations.[5][35]
Another attack in 2008 applying theboomerang 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.[36]
In light of the results for SHA-0, some experts[who?] suggested that plans for the use of SHA-1 in newcryptosystems 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.[37]
In early 2005,Vincent Rijmen andElisabeth 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.[38]
In February 2005, an attack byXiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced.[5] The attacks can find collisions in the full version of SHA-1, requiring fewer than 269 operations. (Abrute-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."[39] 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."[40]
On 17 August 2005, an improvement on the SHA-1 attack was announced on behalf ofXiaoyun Wang,Andrew Yao andFrances Yao at the CRYPTO 2005 Rump Session, lowering the complexity required for finding a collision in SHA-1 to 263.[7] On 18 December 2007 the details of this result were explained and verified by Martin Cochran.[41]
Christophe De Cannière and Christian Rechberger further improved the attack on SHA-1 in "Finding SHA-1 Characteristics: General Results and Applications,"[42] receiving the Best Paper Award atASIACRYPT 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.[43] Their attack was extended further to 73 rounds (of 80) in 2010 by Grechnikov.[44] 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 volunteer computing platformBOINC began August 8, 2007, organized by theGraz University of Technology. The effort was abandoned May 12, 2009 due to lack of progress.[45]
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.[46][47]
In 2008, an attack methodology by Stéphane Manuel reported hash collisions with an estimated theoretical complexity of 251 to 257 operations.[48] 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.[49]
Cameron McDonald, Philip Hawkes and Josef Pieprzyk presented a hash collision attack with claimed complexity 252 at the Rump Session of Eurocrypt 2009.[50] However, the accompanying paper, "Differential Path for SHA-1 with complexityO(252)" has been withdrawn due to the authors' discovery that their estimate was incorrect.[51]
One attack against SHA-1 was Marc Stevens[52] with an estimated cost of $2.77M (2012) to break a single hash value by renting CPU power from cloud servers.[53] Stevens developed this attack in a project called HashClash,[54] 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 257.5 SHA-1 compressions. He estimated this attack could be extended to a full collision with a complexity around 261.
On 8 October 2015, Marc Stevens, Pierre Karpman, and Thomas Peyrin published a freestart collision attack on SHA-1's compression function that requires only 257 SHA-1 evaluations. This does not directly translate into a collision on the full SHA-1 hash function (where an attacker isnot able to freely choose the initial internal state), but undermines the security claims for SHA-1. In particular, it was the first time that an attack on full SHA-1 had beendemonstrated; all earlier attacks were too expensive for their authors to carry them out. The authors named this significant breakthrough in thecryptanalysis of SHA-1The SHAppening.[10]
The method was based on their earlier work, as well as the auxiliary paths (or boomerangs) speed-up technique from Joux and Peyrin, and using high performance/cost efficient GPU cards fromNvidia. The collision was found on a 16-node cluster with a total of 64 graphics cards. The authors estimated that a similar collision could be found by buying US$2,000 of GPU time onEC2.[10]
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 nationalintelligence agencies. As such, the authors recommended that SHA-1 be deprecated as quickly as possible.[10]
On 23 February 2017, theCWI (Centrum Wiskunde & Informatica) and Google announced theSHAttered 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 abirthday 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".[2]
On 24 April 2019 a paper by Gaëtan Leurent and Thomas Peyrin presented at Eurocrypt 2019 described an enhancement to the previously bestchosen-prefix attack inMerkle–Damgård–like digest functions based onDavies–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)[1] 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 theMD5 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).[55] This attack has a memory requirement of 500+ GB.
On 5 January 2020 the authors published an improved attack called "shambles".[8] In this paper they demonstrate a chosen-prefix collision attack with a complexity of 263.4, that at the time of publication would cost US$45K per generated collision.
Implementations of all FIPS-approved security functions can be officially validated through theCMVP program, jointly run by theNational Institute of Standards and Technology (NIST) and theCommunications 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 December 2013[update], 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 (seeSHS Validation ListArchived 2011-08-23 at theWayback Machine).
These are examples of SHA-1message digests in hexadecimal and inBase64 binary toASCII text encoding.
SHA1("The quick brown fox jumps over the lazydog")Even a small change in the message will, with overwhelming probability, result in many bits changing due to theavalanche effect. For example, changingdog tocog produces a hash with different values for 81 of the 160 bits:
SHA1("The quick brown fox jumps over the lazycog")The hash of the zero-length string is:
SHA1("")Pseudocode for the SHA-1 algorithm follows:
Note 1: All variables are unsigned 32-bit quantities and wrap modulo 232 when calculating, except forml, the message length, which is a 64-bit quantity, andhh, the message digest, which is a 160-bit quantity.Note 2: All constants in this pseudo code are inbig endian.Within each word, the most significant byte is stored in the leftmost byte positionInitialize variables:h0 = 0x67452301h1 = 0xEFCDAB89h2 = 0x98BADCFEh3 = 0x10325476h4 = 0xC3D2E1F0ml = 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 inbits iscongruent to −64 ≡ 448 (mod 512)append ml, the original message length in bits, as a 64-bitbig-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 chunksfor each chunk break chunk into sixteen 32-bit big-endian words w[i], 0 ≤ i ≤ 15Message schedule: extend the sixteen 32-bit words into eighty 32-bit words:for ifrom 16 to 79Note 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 1Initialize hash value for this chunk: a = h0 b = h1 c = h2 d = h3 e = h4Main loop:[3][56]for ifrom 0to 79if 0 ≤ i ≤ 19then f = (band c)or ((not b)and d) k = 0x5A827999else if 20 ≤ i ≤ 39 f = bxor cxor d k = 0x6ED9EBA1else if 40 ≤ i ≤ 59 f = (band c)or (band d)or (cand d) k = 0x8F1BBCDCelse if 60 ≤ i ≤ 79 f = bxor cxor d k = 0xCA62C1D6 temp = (aleftrotate 5) + f + e + k + w[i] e = d d = c c = bleftrotate 30 b = a a = tempAdd this chunk's hash to result so far: h0 = h0 + a h1 = h1 + b h2 = h2 + c h3 = h3 + d h4 = h4 + eProduce the final hash value (big-endian) as a 160-bit number:hh = (h0leftshift 128)or (h1leftshift 96)or (h2leftshift 64)or (h3leftshift 32)or h4
The numberhh is the message digest, which can be written in hexadecimal (base 16).
The chosen constant values used in the algorithm were assumed to benothing up my sleeve numbers:
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.h0 throughh3 are the same with the MD5 algorithm, and the fifth (forh4) 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 computef in the main loop above:
Bitwise choice betweenc andd, controlled byb.(0 ≤ i ≤ 19): f = dxor (band (cxor d))(alternative 1)(0 ≤ i ≤ 19): f = (band c)or ((not b)and d)(alternative 2)(0 ≤ i ≤ 19): f = (band 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 = (band c)or (dand (bor c))(alternative 1)(40 ≤ i ≤ 59): f = (band c)or (dand (bxor c))(alternative 2)(40 ≤ i ≤ 59): f = (band c)xor (dand (bxor c))(alternative 3)(40 ≤ i ≤ 59): f = (band c)xor (band d)xor (cand d)(alternative 4)(40 ≤ i ≤ 59): f = vec_sel(c, b, cxor d)(alternative 5)
It was also shown[57] 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 ofw[i] onw[i-3], allows efficient SIMD implementation with a vector length of 4 likex86SSE instructions.
In the table below,internal state means the "internal hash sum" after each compression of a data block.
| Algorithm and variant | Output size (bits) | Internal state size (bits) | Block size (bits) | Rounds | Operations | Security (bits) | Performance onSkylake (mediancpb)[58] | First published | ||
|---|---|---|---|---|---|---|---|---|---|---|
| Long messages | 8 bytes | |||||||||
| MD5 (as reference) | 128 | 128 (4 × 32) | 512 | 4 (16 operations in each round) | And, Xor, Or, Rot,Add (mod 232) | ≤ 18 (collisions found)[59] | 4.99 | 55.00 | 1992 | |
| SHA-0 | 160 | 160 (5 × 32) | 512 | 80 | And, Xor, Or, Rot,Add (mod 232) | < 34 (collisions found) | ≈ SHA-1 | ≈ SHA-1 | 1993 | |
| SHA-1 | < 63 (collisions found)[60] | 3.47 | 52.00 | 1995 | ||||||
| SHA-2 | SHA-224 SHA-256 | 224 256 | 256 (8 × 32) | 512 | 64 | And, Xor, Or, Rot, Shr,Add (mod 232) | 112 128 | 7.62 7.63 | 84.50 85.25 | 2004 2001 |
| SHA-384 | 384 | 512 (8 × 64) | 1024 | 80 | And, Xor, Or, Rot, Shr,Add (mod 264) | 192 | 5.12 | 135.75 | 2001 | |
| SHA-512 | 512 | 256 | 5.06 | 135.50 | 2001 | |||||
| SHA-512/224 SHA-512/256 | 224 256 | 112 128 | ≈ 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[61] | And, Xor, Rot, Not | 112 128 192 256 | 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) | 7.08 8.59 | 155.25 155.50 | |||||
Below is a list of cryptography libraries that support SHA-1:
Hardware acceleration is provided by the following processor extensions:
In the wake of SHAttered, Marc Stevens and Dan Shumow published "sha1collisiondetection" (SHA-1CD), a variant of SHA-1 that detects collision attacks and changes the hash output when one is detected. The false positive rate is 2−90.[63] SHA-1CD is used byGitHub since March 2017 andgit since version 2.13.0 of May 2017.[64]
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.
