Question 1 - 112-51 discussion

SHA-3 is the algorithm that uses a sponge construction where message blocks are XORed into the initial bits of the state that the algorithm then invertible permutes. SHA-3 is a family of cryptographic hash functions that was standardized by NIST in 2015 as a successor to SHA-2. SHA-3 is based on the Keccak algorithm, which won the NIST hash function competition in 2012. SHA-3 uses a sponge construction, which is a simple iterated construction that can produce variable-length output from a fixed-length permutation. The sponge construction operates on a state of b bits, which is divided into two sections: the bitrate r and the capacity c. The sponge construction has two phases: the absorbing phase and the squeezing phase. In the absorbing phase, the input message is padded and divided into blocks of r bits. Each block is XORed into the first r bits of the state, and then the state is transformed by the permutation function f. This process continues until all the input blocks are processed. In the squeezing phase, the output is generated by repeatedly applying the permutation function f to the state and extracting the first r bits as output blocks. The output can be truncated to the desired length. SHA-3 uses a permutation function f that is based on a round function that consists of five steps: theta, rho, pi, chi, and iota. These steps perform bitwise operations, rotations, permutations, and additions on the state. The permutation function f is invertible, meaning that it can be reversed to obtain the previous state. SHA-3 has four variants with different output lengths: SHA3-224, SHA3-256, SHA3-384, and SHA3-512. SHA-3 also supports two additional modes: SHAKE128 and SHAKE256, which are extendable-output functions that can produce arbitrary-length output.

Reference:

Network Defense Essentials Courseware, EC-Council, 2020, pp. 3-23 to 3-25

SHA-3 - Wikipedia, Wikipedia, March 16, 2021

The sponge and duplex constructions - Keccak Team, Keccak Team, 2020