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

2025-07-02

AI Summary

The c-differential uniformity is difficult to apply in block cipher analysis due to multiplicative operations disrupting the key-addition structure. Method: This paper introduces truncated inner c-differential cryptanalysis, which defines inner c-differential pairs ((F(cx oplus a), F(x))) to strictly preserve key-addition invariance and circumvent whitening-key interference; it further establishes a duality between inner c-differential uniformity and outer c-differential uniformity of the inverse function. Contribution/Results: For the first time, this approach enables practical application of c-differential uniformity on the full 9-round Kuznyechik. Leveraging large-scale differential statistics and a multidimensional testing framework, we detect significant non-randomness—observed biases reach up to 1.7× the expected value, with corrected p-values as low as (1.85 imes 10^{-3}). This yields the first effective distinguisher against the full 9-round Kuznyechik.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Content-based information diffusion

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 $(F(xoplus a), cF(x))$, 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: $(F(cxoplus a), F(x))$. 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 $1.7 imes$ and corrected p-values as low as $1.85 imes 10^{-3}$, suggesting insufficient security margin against this new attack vector. This represents the first practical distinguisher against the full 9-round Kuznyechik.

Problem

• Develops inner c-differential cryptanalysis for block ciphers
• Resolves structural disruption from c-differential uniformity
• Demonstrates practical attack on full 9-round Kuznyechik cipher

Innovation

• Truncated inner c-differential cryptanalysis technique
• Inner c-differential preserves cipher structure
• Multi-faceted statistical-computational framework implementation