Wenxiao Qiao, Siwei Sun, Ying Chen, et al., “New coefficient grouping for complex affine layers,” Chinese Journal of Electronics, vol. 34, no. 2, pp. 1–13, 2025. DOI: 10.23919/cje.2023.00.373
Citation: Wenxiao Qiao, Siwei Sun, Ying Chen, et al., “New coefficient grouping for complex affine layers,” Chinese Journal of Electronics, vol. 34, no. 2, pp. 1–13, 2025. DOI: 10.23919/cje.2023.00.373

New Coefficient Grouping for Complex Affine Layers

  • Recently, designing symmetric primitives for applications in cryptographic protocols including multi-party computation, fully homomorphic encryption, and zero-knowledge proofs has become an important research topic. Among many such new symmetric schemes, a power function over a large finite field \mathbbF_q is commonly used. In this paper, we revisit the algebraic degree’s growth for a substitution-permutation network (SPN) cipher over \mathbbF_2^n (n\ge3) , whose S-box is defined as a composition of a power function P(x)=x^2^d+1 where d\ge1 with a polynomial A(x)=a_0+ \sum\limits_w=1^Wa_wx^2^\beta_w where a_i\in\mathbbF_2^n for 0\le i\le W and a_w\neq0 for 1\le w\le W . We propose a new coefficient grouping technique, which is based on our new description of the monomials that will probably appear in the state. Specifically, we propose a new measure to find proper (\beta_1,\beta_2,\dots,\beta_W) for the algebraic degree’s fastest growth and a new method to compute the algebraic degree’s upper bound for arbitrary A(x) . Especially for Chaghri, which was presented at ACM CCS 2022, we obtained a tighter upper bound on the algebraic degree.
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