Security Evaluation of SHA-3
The Keccak hash function family was designed by Bertoni et al. and standardized as SHA-3 in 2015 by the National Institute of Standards and Technology of the U.S. (NIST). In this page, major cryptanalysis results against round-reduced Keccak/SHA-3 are listed, including collision attacks, preimage attacks, key recovery attacks on keyed schemes based on the Keccak permutation Keccak-p, as well as distinguishers against Keccak-p.
2. Collision Attacks
2.1 Collision attacks on Keccak/SHA-3
The standard SHA-3 and the original Keccak design differ only in the way of message padding, and hence share almost all security analysis. The internal state of Keccak or SHA-3 is of 1600 bits.
2.2 Practical collision attacks on instances of the Keccak Challenge
To promote cryptanalysis against Keccak, the Keccak team proposed variants with lower security levels in the Keccak Challenge, where the size of the internal state varies from 200 up to 1600 bits, the capacity is of 160 bits and the output is truncated to 160 bits for collision challenges.
3. Preimage Attacks
3.1 Preimage attacks on Keccak/SHA-3
3.2 Practical preimage attacks on instances of the Keccak Challenge
To promote cryptanalysis against Keccak, the Keccak team proposed variants with lower security levels in the Keccak Challenge, where the size of the internal state varies from 200 up to 1600 bits, the capacity is of 160 bits and the output is truncated to 80 bits for collision challenges.
4. Key Recovery Attacks
KMAC128/256, SHA-3 based MAC recommended by NIST, where the key is processed as an independent block before absorbing message blocks
Keccak-MAC, taking K||M as input
4.2 Authenticated Encryptions
Keyak and Ketje are two Keccak-p based authenticatedencryption schemes.
Note: NR means nonce-respected
4.3 Pseudorandom Function
Farfalle is a construction for pseudorandom functions (PRF) with variable input and output length, and Kravatte is an instantiation of it by taking Keccak-p as the underlying permutations.
Farfalle consists of three steps:
We exploit the properties of Farfalle and in the attacks on Kravatte only the number of rounds in the expansion layer matters. There are two permutations in the expansion layer, pd and pe. Let the number of rounds in pd and pe be nd, ne respectively. In the ePrint/ECC version of Kravatte, (nd, ne) = (4, 4)/(6,6).
Due to this attack, the designers of Kravatte replaced the linear roll function in the expansion layer with a non-linear one and increased nd and ne from 4 to 6.
5.1 Differential Distinguishers
The differential distinguishers are mainly based on the differential properties, including the rebound-like distinguisher connecting two short differential paths under the limited birthday setting , and internal differential distinguisher .
5.2 Algebraic Distinguishers
The algebraic distinguishers mainly take advantage of the low algebraic degree of the Keccak Chi operation (the only nonlinear operation) -- 2 and 3 in the forward and backward directions . They take an inside-out approach, which gains 2 or 3 rounds from the middle at the starting point, by the technique of linear structures.
6. Differential Propagation Analysis
The lower bounds on differential propagation weight of Keccak-f for 2/3-round differential trails are 8 and 32 . For the permutation Keccak-f, 3-round trails of propagation weight no greater than 53 are exhaustively searched giving better lower bounds for 4/5/6-round and full rounds trails . Lower bounds on differential trails of other Keccak-f permutations are summarized in .
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