[Resource Topic] 2017/165: SymSum: Symmetric-Sum Distinguishers Against Round Reduced SHA3

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SymSum: Symmetric-Sum Distinguishers Against Round Reduced SHA3

Authors: Dhiman Saha, Sukhendu Kuila, Dipanwita Roy Chowdhury


In this work we show the existence of special sets of inputs for which the sum of the images under SHA3 exhibits a symmetric property. We develop an analytical framework which accounts for the existence of these sets. The framework constitutes identification of a generic property of iterated SPN based functions pertaining to the round-constant addition and combining it with the notion of $m-$fold vectorial derivatives for differentiation over specially selected subspaces. Based on this we propose a new distinguisher called SymSum for the SHA3 family which penetrates up to 9 rounds and outperforms the ZeroSum distinguisher by a factor of four. Interestingly, the current work is the first analysis of SHA3/Keccak that relies on round-constants but is independent of their Hamming-weights.

ePrint: https://eprint.iacr.org/2017/165

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