Paper 2026/1528 Original: eprint.iacr.org/2026/1528 ↗

Revisiting Automated Quantum Periodic Distinguisher Construction

Abstract

Simon's algorithm can detect hidden XOR periods in functions derived from symmetric ciphers. Finding such functions becomes difficult when nonlinear layers and diffusion spread the relevant expressions across many branches, so recent work has used symbolic search to automate the construction. We refine the algebraic SMT model of Liu et al. in two ways. Prefix realization checks whether a symbolic starting state can be reached through preceding rounds and records the round-key nibbles needed to produce it. DDT Filtering restricts a local S-box input to a DDT bucket so that the symbolic path can cross an additional nonlinear layer. The latter condition is key-dependent: the target period need not lie in the translation space of the selected bucket, and our results state this condition explicitly. We report the maximum round counts found for GFS-2F, GFS-4F, Skipjack-B, LBlock, TWINE, CRAFT, and SKINNY, with Liu et al.'s automated model as the main comparison. We also combine selected witnesses with partial round-key guesses in the Grover–meet–Simon setting, yielding reduced-round key-recovery candidates below the corresponding comparison budgets.