## Cryptology ePrint Archive: Report 2018/1107

Further observations on SIMON and SPECK families of block ciphers

S. M. Dehnavi

Abstract: SIMON and SPECK families of block ciphers are well-known lightweight ciphers designed by NSA. In this note, based on the previous investigations on SIMON, a closed formula for the squared correlations and differential probabilities of the mapping $\phi(x) = x \odot S^1(x)$ on $\mathbb{F}_2^n$ is given. From the aspects of linear and differential cryptanalysis, this mapping is equivalent to the core quadratic mapping of SIMON via rearrangement of coordinates and EA-equivalence. Based upon the proposed explicit formula, a full description of DDT and LAT of $\phi$ is provided. In the case of SPECK, as the only nonlinear operation in this family of ciphers is, addition mod $2^n$, after reformulating the formula for linear and differential probabilities of addition mod $2^n$, straightforward algorithms for finding the output masks with maximum squared correlation, given the input masks as well as the output differences with maximum differential probability, given the input differences, are presented.

Category / Keywords: secret-key cryptography / SIMON, SPECK, DDT, LAT, Pseudo-octal representation, Gaps and blocks representation, Modular addition mod $2^n$