The SHA-2 family was released in 2001 in a set of four hashing algorithms: 224, 256, 384, and 512 bits. NIST is currently pushing for the use of SHA-2 algorithms due to the ability for computers to find SHA-1 collisions.
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The algorithms are basically identical (like a 'family') to each other in many ways:
All Inputs are in ASCII
Indexes start from 0 and end at length-1
Functions:
rot_right(a,n): take the last n bits of a and move them to the front (not the same as a>>n)
a>>n:a shifted to the right n bits
AND,OR, NOT, and XOR are bitwise functions
Addition is done mod 2^32 for SHA-224 and 256 and 2^64 for for SHA-348 and 512
Defined in a PDF from NIST:
S0(value) = rot_right(value,2) xor rot_right(value,13) xor rot_right(value,22)
S1(value) = rot_right(value,6) xor rot_right(value,11) xor rot_right(value,25)
s0(value) = rot_right(value,7) xor rot_right(value,18) xor value»3
s1(value) = rot_right(value,17) xor rot_right(value,19) xor value»10
Ch(m,n,o) = (m and n) xor (not(m) and o)
Maj(m,n,o) = (m and n) xor (m and o) xor (n and o)
Preprocessing:
1. Change the input into binary
2. Get the length of the binary string -> L
3. Add a '1' to the end of the data
4. Add '0's to the end of the data until the length of the data
mod 448 = 0, for SHA-224 and 256
mod 512 = 0, for SHA-348 and 512
5. Divide the total length of the data by
448 for SHA-224 and 256
896 for SHA-348 and 512
to get the number of rounds i
6. Change L into binary and add as many 0s in front of it as possible until the length of (data + L) is
mod 512 = 0 for SHA-224 and 256
mod 1024 = 0 for SHA-348 and 512
7. Put together the data and the expanded L
8. Split the data into
512 bit blocks for SHA-224 and 256
1024 bit blocks for SHA-348 and 512
called 'W' in the NIST paper
9. For 1 ≤ n ≤ i-1
Split Wn into 16 parts of
32 bits for SHA-224 and 256
64 bits for SHA-348 and 512
creating the lists called List n (n = 0,1,2,...)
r = 63 for SHA-224 and 256
79 for SHA-348 and 512
Expand List n
For 16 ≤ x ≤ r
List n [x] = s1([x-2]) + [x-7] + s0([x-15]) + [x-16] \\List n at index [x-a], not the number [x-a]
Core Function
For n from 0 ≤ n < i
set:
a = h0
b = h1
c = h2
d = h3
e = h4
f = h5
g = h6
h = h7
For x from 0 ≤ x ≤ 63 for SHA-224 and 256
80 for SHA-384 and 512
t1 = h + S1(e) + Ch(e,f,g) + k[x] + List n [x]
t2 = S0(a) + Maj(a,b,c)
h = g
g = f
f = e
e = d + t1
d = c
c = b
b = a
a = t1 + t2
After the x rounds
h0 = a + h0
h1 = b + h1
h2 = c + h2
h3 = d + h3
h4 = e + h4
h5 = f + h5
h6 = g + h6
h7 = h + h7
if there is more data:
run the core function again, but do not reset h0,h1,h2,h3,h4,h5,h6,h7. Use the values from the previous round and use the next list
Differences
Data Size
2^32 bit values for SHA-224 and 256
2^64 bit values for SHA-384 and 512
Initial Values:
SHA-224
h0 = 0xc1059ed8
h1 = 0x367cd507
h2 = 0x3070dd17
h3 = 0xf70e5939
h4 = 0xffc00b31
h5 = 0x68581511
h6 = 0x64f98fa7
h7 = 0xbefa4fa4
SHA-256
h0 = 0x6a09e667
h1 = 0xbb67ae85
h2 = 0x3c6ef372
h3 = 0xa54ff53a
h4 = 0x510e527f
h5 = 0x9b05688c
h6 = 0x1f83d9ab
h7 = 0x5be0cd19
SHA-512
h0 = 0x6a09e667f3bcc908
h1 = 0xbb67ae8584caa73b
h2 = 0x3c6ef372fe94f82b
h3 = 0xa54ff53a5f1d36f1
h4 = 0x510e527fade682d1
h5 = 0x9b05688c2b3e6c1f
h6 = 0x1f83d9abfb41bd6b
h7 = 0x5be0cd19137e2179
SHA-384
h0 = 0xcbbb9d5dc1059ed8
h1 = 0x629a292a367cd507
h2 = 0x9159015a3070dd17
h3 = 0x152fecd8f70e5939
h4 = 0x67332667ffc00b31
h5 = 0x8eb44a8768581511
h6 = 0xdb0c2e0d64f98fa7
h7 = 0x47b5481dbefa4fa4
Constant List k
SHA-224 and 256
[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]
SHA-384 and 512
[0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc,
0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118,
0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2,
0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694,
0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,
0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,
0x983e5152ee66dfab, 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4,
0xc6e00bf33da88fc2, 0xd5a79147930aa725, 0x06ca6351e003826f, 0x142929670a0e6e70,
0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed, 0x53380d139d95b3df,
0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b,
0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30,
0xd192e819d6ef5218, 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8,
0x19a4c116b8d2d0c8, 0x1e376c085141ab53, 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8,
0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,
0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec,
0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b,
0xca273eceea26619c, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178,
0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b,
0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c,
0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817]
Output
All 'h's are strings, not values
SHA-224
h0 + h1 + h2 + h3 + h4 + h5 +h6
SHA-256
h0 + h1 + h2 + h3 + h4 + h5 +h6 + h7
SHA-384
h0 + h1 + h2 + h3 + h4 + h5
SHA-512
h0 + h1 + h2 + h3 + h4 + h5 +h6 + h7
Other sites
PDF from NIST
Another Crypto Site
An online calculator for multiple hashes
