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

• URL: http://arxiv.org/abs/2507.02181v1
• Date: Wed, 02 Jul 2025 22:27:33 GMT
• Title: Extended c-differential distinguishers of full 9 and reduced-round Kuznyechik cipher
• Authors: Pantelimon Stanica, Ranit Dutta, Bimal Mandal,
• Abstract summary: This paper introduces em truncated inner $c$-differential cryptanalysis, a novel technique that for the first time enables the practical application of $c$-differential uniformity to block ciphers.<n>Our main contribution is a comprehensive multi-faceted statistical-computational framework, implementing truncated $c$-differential analysis against the full 9-round Kuznyechik cipher.
• Score: 3.3311266423308252
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces {\em 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 $(F(x\oplus a), cF(x))$, 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 \emph{inner} $c$-differential approach where multiplication by $c$ affects the input: $(F(cx\oplus a), F(x))$. 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 (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 $1.7\times$ and corrected p-values as low as $1.85 \times 10^{-3}$, suggesting insufficient security margin against this new attack vector. This represents the first practical distinguisher against the full 9-round Kuznyechik.

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