Everything about Sha-1 totally explained
The
SHA hash functions are five
cryptographic hash functions designed by the
National Security Agency (NSA) and published by the
NIST as a U.S.
Federal Information Processing Standard. SHA stands for
Secure Hash Algorithm. Hash algorithms compute a fixed-length digital representation (known as a
message digest) of an input data sequence (the
message) of any length. They are called “secure” when:
- It is computationally infeasible to find a message that corresponds to a given message digest.
- It is computationally infeasible to find two different messages that produce the same message digest.
- Any change to a message (including single bit changes) will, with an exceedingly high probability, result in a completely different message digest.
The five algorithms are denoted SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512. The latter four variants are sometimes collectively referred to as SHA-2. SHA-1 produces a message digest that's 160 bits long; the number in the other four algorithms' names denote the bit length of the digest they produce.
SHA-1 is employed in several widely used security applications and protocols, including
TLS and
SSL,
PGP,
SSH,
S/MIME, and
IPsec. It was considered to be the successor to
MD5, an earlier, widely-used hash function.
The security of SHA-1 has been somewhat compromised by cryptography researchers. Although no attacks have yet been reported on the SHA-2 variants, they're algorithmically similar to SHA-1 and so efforts are underway to develop improved alternative hashing algorithms. An open competition for a new SHA-3 function was formally announced in the
Federal Register on November 2, 2007. "NIST is initiating an effort to develop one or more additional hash algorithms through a public competition, similar to the
development process for the
Advanced Encryption Standard (AES)." Submissions are due October 31, 2008 and the proclamation of a winner and publication of the new standard are scheduled to take place in 2012.
SHA-0 and SHA-1
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 2
32. ]]
The original specification of the algorithm was published in 1993 as the
Secure Hash Standard,
FIPS PUB 180, by US 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 It was withdrawn by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 didn't 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.
SHA-1 (as well as SHA-0) produces a 160-bit digest from a
message with a maximum length of (2
64 − 1) bits and is based on principles similar to those used by
Ronald L. Rivest of
MIT in the design of the
MD4 and
MD5 message digest algorithms.
Cryptanalysis
For a hash function which violates the first criterion listed above, finding a message that corresponds to a given message digest can always be done using a brute force search in 2
L evaluations, where
L is the number of bits in the message digest. This is called a
preimage attack and may or may not be practical in a particular computing environment. The second criterion, finding two different messages that produce the same message digest, known as a
collision, requires on average only 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 2
80 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 has 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 (typically in the
shadow file) which may or may not be trivial. Reversing password encryption (for example to obtain a password to try against a user's account elsewhere) isn't made possible by the attacks.
In the case of document signing, an attacker couldn't 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.
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 2
61, fewer than the 2
80 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 2
51 and took about 80,000 CPU hours on a
supercomputer with 256
Itanium 2 processors.
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 2
40, 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 2
39 operations.
SHA-1
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.
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 2
80 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 2
69 operations. (A
brute-force search would require 2
80 operations.)
The authors write:
"In particular, our analysis is built upon the original differential attack on SHA0 [
sic], the near collision attack on SHA0, the multiblock collision techniques, as well as the message modification techniques used in the collision search attack on MD5. Breaking SHA1 wouldn't be possible without these powerful analytical techniques.". The authors have presented a collision for 58-round SHA-1, found with 2
33 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 isn't 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 2
63. 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 2
35 compression function evaluations.
As this attack requires the equivalent of about 2
35 evaluations, it's considered to be a significant theoretical break. To find an actual collision, however, a massive distributed computing effort or very large parallel supercomputer such as those possessed by
NSA would be required. To that end, a collision search for SHA-1 using the distributed computing platform
BOINC is currently being made by the
Graz University of Technology.
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.
SHA-2
NIST published four additional hash functions in the SHA family, each with longer digests, collectively known as SHA-2. However the term SHA-2 officially isn't standardized.
The individual variants are named after their digest lengths (in bits): SHA-224, SHA-256, SHA-384, and SHA-512. The latter three were first published in 2001 in the draft FIPS PUB 180-2, at which time review and comment were accepted. FIPS PUB 180-2, which also includes SHA-1, was released as an official standard in 2002. In February 2004, a change notice was published for FIPS PUB 180-2, specifying an additional variant, SHA-224, defined to match the key length of two-key
Triple DES. These variants are patented in . The
United States representing NSA, has released the patent under a royalty free license.
SHA-256 and SHA-512 are novel hash functions computed with 32- and 64-bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA-224 and SHA-384 are simply truncated versions of the first two, computed with different initial values.
These new hash functions have not received as much scrutiny by the public cryptographic community as SHA-1 has, and so their cryptographic security isn't yet as well-established. Gilbert and Handschuh (2003) have studied the newer variants and found no weaknesses.
SHA sizes
In the table below,
internal state means the “internal hash sum” after each compression of a data block; see
Merkle-Damgård construction for more details.
| Algorithm |
Output size (bits) |
Internal state size (bits) |
Block size (bits) |
Max message size (bits) |
Word size (bits) |
Rounds |
Operations |
Collision
|
| SHA-0 |
160 |
160 |
512 |
264 − 1 |
32 |
80 |
+,and,or,xor,rotl |
Yes |
| SHA-1 |
160 |
160 |
512 |
264 − 1 |
32 |
80 |
+,and,or,xor,rotl |
263 attack |
| SHA-256/224 |
256/224 |
256 |
512 |
264 − 1 |
32 |
64 |
+,and,or,xor,shr,rotr |
None |
| SHA-512/384 |
512/384 |
512 |
1024 |
2128 − 1 |
64 |
80 |
+,and,or,xor,shr,rotr |
None
|
Applications
SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512 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.
A prime motivation for the publication of the Secure Hash Algorithm was the
Digital Signature Standard, in which it's incorporated.
The SHA hash functions have been used as the basis for the
SHACAL block ciphers.
Example hashes
The following is an example of SHA-1 digests.
ASCII encoding is assumed for all messages.
SHA1("
The quick brown fox jumps over the lazy dog")
= 2fd4e1c6 7a2d28fc ed849ee1 bb76e739 1b93eb12
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:
SHA1("The quick brown fox jumps over the lazy
cog")
= de9f2c7f d25e1b3a fad3e85a 0bd17d9b 100db4b3
Official validation
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 doesn't replace in any way the formal CMVP validation, which is required by law for certain applications.
As of October 2006, there are more than 500 validated implementations of SHA-1, with fewer than ten of them capable of handling messages with a length in bits not a multiple of eight (see
SHS Validation List). It is also important to note that some implementations available on the Internet don't digest the NIST validation vectors correctly, although they may correctly process the examples listed in the SHA-1 standard.
SHA-1 algorithm
Pseudocode for the SHA-1 algorithm follows:
Note: All variables are unsigned 32 bits and wrap modulo 232 when calculating
Initialize variables:
h0 = 0x67452301
h1 = 0xEFCDAB89
h2 = 0x98BADCFE
h3 = 0x10325476
h4 = 0xC3D2E1F0
Pre-processing:
append the bit '1' to the message
append k bits '0', where k is the minimum number ≥ 0 such that the resulting message
length (in
bits) is
congruent to 448 (mod 512)
append length of message (before pre-processing), in
bits, as 64-bit
big-endian integer
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):
digest = hash = h0
append h1
append h2
append h3
append h4
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)
(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)
SHA-256 (one of the SHA-2 versions) algorithm
Pseudocode for the SHA-256 algorithm follows. Note the great increase in mixing between bits of the
w[16..63] words compared to SHA-1.
Note: All variables are unsigned 32 bits and wrap modulo 232 when calculating
Initialize variables
(first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19):
h0 := 0x6a09e667
h1 := 0xbb67ae85
h2 := 0x3c6ef372
h3 := 0xa54ff53a
h4 := 0x510e527f
h5 := 0x9b05688c
h6 := 0x1f83d9ab
h7 := 0x5be0cd19
Initialize table of round constants
(first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311):
k[0..63] :=
0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
Pre-processing:
append the bit '1' to the message
append k bits '0', where k is the minimum number >= 0 such that the resulting message
length (in
bits) is
congruent to 448 (mod 512)
append length of message (before pre-processing), in
bits, as 64-bit big-endian integer
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[0..15]
Extend the sixteen 32-bit words into sixty-four 32-bit words:
for i
from 16 to 63
s0 := (w[i-15]
rightrotate 7)
xor (w[i-15]
rightrotate 18)
xor (w[i-15]
rightshift 3)
s1 := (w[i-2]
rightrotate 17)
xor (w[i-2]
rightrotate 19)
xor (w[i-2]
rightshift 10)
w[i] := w[i-16]
+ s0
+ w[i-7]
+ s1
Initialize hash value for this chunk:
a := h0
b := h1
c := h2
d := h3
e := h4
f := h5
g := h6
h := h7
Main loop:
for i
from 0 to 63
s0 := (a
rightrotate 2)
xor (a
rightrotate 13)
xor (a
rightrotate 22)
maj := (a
and b)
xor (a
and c)
xor (b
and c)
t2 := s0 + maj
s1 := (e
rightrotate 6)
xor (e
rightrotate 11)
xor (e
rightrotate 25)
ch := (e
and f)
xor ((
not e)
and g)
t1 := h + s1 + ch + k[i] + w[i]
h := g
g := f
f := e
e := d + t1
d := c
c := b
b := a
a := t1 + t2
Add this chunk's hash to result so far:
h0 := h0 + a
h1 := h1 + b
h2 := h2 + c
h3 := h3 + d
h4 := h4 + e
h5 := h5 + f
h6 := h6 + g
h7 := h7 + h
Produce the final hash value (big-endian):
digest = hash = h0
append h1
append h2
append h3
append h4
append h5
append h6
append h7
The
ch and
maj functions can be optimized the same way as described for SHA-1.
SHA-224 is identical to SHA-256, except that:
the initial variable values h0 through h7 are different, and
the output is constructed by omitting h7.
SHA-512 is identical in structure, but:
all numbers are 64 bits long,
there are 80 rounds instead of 64,
the initial values and additive constants are extended to 64 bits, and
the shift and rotate amounts used are different.
SHA-384 is identical to SHA-512, except that:
the initial values h0 through h7 are different, and
the output is constructed by omitting h6 and h7.Further Information
Get more info on 'Sha-1'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://sha_hash_functions.totallyexplained.com">SHA hash functions Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
