The cryptographic sponge is a construction scheme for hash functions (and other symmetric primitives) based on an unkeyed permutation. The most famous example is Keccak, which won the SHA-3 competition.
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Why are the constants so simple in Keccak?
Keccak, the construction selected for SHA-3 is very interesting. It seems unlike other primitives and has chosen very simple constants. (Keccak talk PDF)
The initial values of the state in Keccak is ...
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Why xor the message into the state for sponge hashes?
Sponge hashes like Keccak(SHA-3) and CubeHash, xor a message block into part of the internal state. Why use a reversible operation like xor for that, instead of replacing that part of the state with ...