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Secure Hash Algorithm 2 (SHA-2)#

The Secure Hash Algorithm 2 (SHA2) is a set of 6 cryptographic hash functions with 224, 256, 384 or 512 bits.

Variant Block State Rounds Output
SHA2-224 512 b 256 b 64 224 b
SHA2-245 512 b 256 b 64 256 b
SHA2-384 1024 b 512 b 80 384 b
SHA2-512 1024 b 512 b 80 512 b

Applications: TLS/SSL, PGP, SSH, S/MIME, and IPsec.

SHA2-256 (\" \") =

e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855

Working Principle#

A message is processed by blocks of 512 = 16 × 32 bits, each block requiring 64 rounds. For SHA-256 each round calculates 8 intermediate 32bit hash values.

One round of the SHA2 compression

  1. Padding: ensure that the message length is a multiple of 512 bits

  2. Block decomposition: Parse the message into \(N\) 512-bit blocks \(M_i\)

  3. Hash computation: Process one block at a time an iteratively compute

    1. Create 64 chunks \(w_i\) of 32 bit and copy the block into it
    2. Initialize the internal state \([a, b, c, d, e, f, g, h]\)

    3. For every chunk \(w_i\):

    4. \(\text{CH}( e, f, g ) = (e \land f) \oplus (\neg e \land g)\)

    5. \(\text{Ma}( a, b, c) = (a \land b) \oplus (a \land c) \oplus ( b \land c)\)
    6. \(\Sigma_{0}(a) = (a \ggg 2) \oplus (a \ggg 13) \oplus (a \ggg 22)\)
    7. \(\Sigma_{1}(e) = (e \ggg 6) \oplus (e \ggg 11) \oplus (e \ggg 25)\)

SHA2-256#

Initial hash values:

h[0..7] := 0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a,
           0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19

Test Vectors#

x  = 0x   // empty, "", length 0
SHA2-224( x ) = 0x d14a028c2a3a2bc9476102bb288234c415a2b01f828ea62ac5b3e42f
SHA2-256( x ) = 0x e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855
SHA2-384( x ) = 0x
38b060a751ac96384cd9327eb1b1e36a21fdb71114be07434c0cc7bf63f6e1da274edebfe76f65fbd51ad2f14898b95b
SHA2-512( x ) = 0x
cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e

References#