Extended c-differential distinguishers of full 9 and reduced-round Kuznyechik cipher

This paper introduces { truncated inner c-differential cryptanalysis}, a novel technique that for the first time enables the practical application of c-differential uniformity to block ciphers. While Ellingsen et al. (IEEE Trans. Inf. Theory, 2020) established the notion of c-differential uniformity using (F(x⊕ a), cF(x)), a key challenge remained: multiplication by c disrupts the structural properties essential for block cipher analysis, particularly key addition. We resolve this challenge by developing an inner c-differential approach where multiplication by c affects the input: (F(cx⊕ a), F(x)). We prove that the inner c-differential uniformity of a function F equals the outer c-differential uniformity of F⁻¹, establishing a fundamental duality. This modification preserves cipher structure while enabling practical cryptanalytic applications. Our main contribution is a comprehensive multi-faceted statistical-computational framework, implementing truncated c-differential analysis against the full 9-round Kuznyechik cipher with no key pre-whitening (the inner c-differentials are immune to the key whitening at the backend). Through extensive computational analysis involving millions of differential pairs, we demonstrate statistically significant non-randomness across all tested round counts. For the full 9-round cipher, we identify multiple configurations triggering critical security alerts, with bias ratios reaching 1.7× and corrected p-values as low as 1.85 × 10⁻³, suggesting insufficient security margin against this new attack vector. This represents the first practical distinguisher against a full 9-round Kuznyechik variant.