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What Is Domain Separation In Hashing? Meet cSHAKE

NIST held a competition for a hashing function to replace SHA-1 and SHA-2, and select Keccak as the winner. It has since been defined as SHA-3 within FIP 202. The following are test vectors for “abc” [Test vectors][Sample]:

SHA-3-224	e642824c3f8cf24a d09234ee7d3c766f c9a3a5168d0c94ad 73b46fdf
SHA-3-256	3a985da74fe225b2 045c172d6bd390bd 855f086e3e9d525b 46bfe24511431532
SHA-3-384	ec01498288516fc9 26459f58e2c6ad8d f9b473cb0fc08c25 96da7cf0e49be4b2 98d88cea927ac7f5 39f1edf228376d25
SHA-3-512	b751850b1a57168a 5693cd924b6b096e 08f621827444f70d 884f5d0240d2712e 10e116e9192af3c9 1a7ec57647e39340 57340b4cf408d5a5 6592f8274eec53f0

and for “” it is:

SHA-3-224	6b4e03423667dbb7 3b6e15454f0eb1ab d4597f9a1b078e3f 5b5a6bc7
SHA-3-256	a7ffc6f8bf1ed766 51c14756a061d662 f580ff4de43b49fa 82d80a4b80f8434a
SHA-3-384	0c63a75b845e4f7d 01107d852e4c2485 c51a50aaaa94fc61 995e71bbee983a2a c3713831264adb47 fb6bd1e058d5f004
SHA-3-512	a69f73cca23a9ac5 c8b567dc185a756e 97c982164fe25859 e0d1dcc1475c80a6 15b2123af1f5f94c 11e3e9402c3ac558 f500199d95b6d3e3 01758586281dcd26

The interesting thing about SHA-3 is that it stores a state value, and we can thus use it to synchronise messages (and where each side has the same state, given secret initialisation values). This state (S) is defined with a 5 × 5 array of w-bit…