Paper 2017/165

SymSum: Symmetric-Sum Distinguishers Against Round Reduced SHA3

Dhiman Saha, Sukhendu Kuila, and 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.

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Publication info
Published by the IACR in TOSC 2017
distinguisherKeccakSHA3hash functionscryptanalysiszero-sumsself-symmetryvectorial derivatives
Contact author(s)
saha dhiman @ gmail com
2017-02-24: revised
2017-02-23: received
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      author = {Dhiman Saha and Sukhendu Kuila and Dipanwita Roy Chowdhury},
      title = {SymSum: Symmetric-Sum Distinguishers Against Round Reduced SHA3},
      howpublished = {Cryptology ePrint Archive, Paper 2017/165},
      year = {2017},
      note = {\url{}},
      url = {}
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