Paper 2023/1426

Arithmetic Circuit Implementations of S-boxes for SKINNY and PHOTON in MPC

Aysajan Abidin, KU Leuven
Erik Pohle, KU Leuven
Bart Preneel, KU Leuven

Secure multi-party computation (MPC) enables multiple distrusting parties to compute a function while keeping their respective inputs private. In a threshold implementation of a symmetric primitive, e.g., of a block cipher, each party holds a share of the secret key or of the input block. The output block is computed without reconstructing the secret key. This enables the construction of distributed TPMs or transciphering for secure data transmission in/out of the MPC context. This paper investigates implementation approaches for the lightweight primitives SKINNY and PHOTON in arithmetic circuits. For these primitives, we identify arithmetic expressions for the S-box that result in smaller arithmetic circuits compared to the Boolean expressions from the literature. We validate the optimization using a generic actively secure MPC protocol and obtain 18% faster execution time with 49% less communication data for SKINNY-64-128 and 27% to 74% faster execution time with 49% to 81% less data for PHOTON $P_{100}$ and $P_{288}$. Furthermore, we find a new set of parameters for the heuristic method of polynomial decomposition, introduced by Coron, Roy and Vivek, specialized for SKINNY's 8-bit S-box. We reduce the multiplicative depth from 9 to 5.

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Publication info
Published elsewhere. Minor revision. ESORICS 2023
S-boxSKINNYPHOTONMPCArithmetic Circuit
Contact author(s)
aysajan abidin @ esat kuleuven be
erik pohle @ esat kuleuven be
bart preneel @ esat kuleuven be
2023-09-24: approved
2023-09-20: received
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      author = {Aysajan Abidin and Erik Pohle and Bart Preneel},
      title = {Arithmetic Circuit Implementations of S-boxes for SKINNY and PHOTON in MPC},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1426},
      year = {2023},
      note = {\url{}},
      url = {}
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