Abstract In recent years, progress in practical applications of multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge proofs (ZKP) motivates people to explore symmetric-key cryptographic algorithms, as well as corresponding cryptanalysis techniques (such as differential cryptanalysis, linear cryptanalysis), over finite Abelian groups or prime fields $${\mathbb {F}}_p$$ F p for large p . In this paper, we establish the links between linear cryptanalysis and differential cryptanalysis over general finite Abelian groups. As the first application, we revisit linear cryptanalysis and give general results of linear approximations over arbitrary finite Abelian groups. More precisely, we consider the linearity , which is the maximal non-trivial linear approximation, to characterize the resistance of a function against linear cryptanalysis. This thereby generalizes the work of Pott in 2004 and completes the generalization of Sidelnikov–Chabaud–Vaudenay’s bound from $${\mathbb {F}}_2^n$$ F 2 n to finite Abelian groups. As the second application, we give an exact expression for the correlation of differential-linear approximations over arbitrary finite Abelian groups ( $${\mathbb {F}}_p^n$$ F p n ) under the sole assumption that the two parts of the cipher are independent of each other. In particular, we completely generalize the differential-linear cryptanalysis from $${\mathbb {F}}_2^n$$ F 2 n to arbitrary finite Abelian groups ( $${\mathbb {F}}_p^n$$ F p n ).

Abstract The differential-linear attack, combining the power of the two most effective techniques for symmetric-key cryptanalysis, was proposed by Langford and Hellman at CRYPTO 1994. From the exact formula for evaluating the bias of a differential-linear distinguisher (JoC 2017), to the differential-linear connectivity table technique for dealing with the dependencies in the switch between the differential and linear parts (EUROCRYPT 2019), and to the improvements in the context of cryptanalysis of ARX primitives (CRYPTO 2020, EUROCRYPT 2021), we have seen significant development of the differential-linear attack during the last four years. In this work, we further extend this framework by replacing the differential part of the attack by rotational-XOR differentials. Along the way, we establish the theoretical link between the rotational-XOR differential and linear approximations and derive the closed formula for the bias of rotational differential-linear distinguishers, completely generalizing the results on ordinary differential-linear distinguishers due to Blondeau, Leander, and Nyberg (JoC 2017) to the case of rotational differential-linear cryptanalysis. We then revisit the rotational cryptanalysis from the perspective of differential-linear cryptanalysis and generalize Morawiecki et al.’s technique for analyzing , which leads to a practical method for estimating the bias of a (rotational) differential-linear distinguisher in the special case where the output linear mask is a unit vector. Finally, we apply the rotational differential-linear technique to the cryptographic permutations involved in , , , and . This gives significant improvements over existing cryptanalytic results, or offers explanations for previous experimental distinguishers without a theoretical foundation. To confirm the validity of our analysis, all distinguishers with practical complexities are verified experimentally. Moreover, we discuss the possibility of applying the rotational differential-linear technique to S-box-based designs or keyed primitives, and propose some open problems for future research.

Wireless body area networks (WBANs) are applied to monitor patients remotely. The sensors in WBANs have the characteristics of limited computing and less memory, while requiring real-time and security communications between sensors. In order to deal with the above problems, this article proposes a new asymmetric cryptographic algorithm (Diffie-Hellman-Hash-compression, abbreviated as DHS-C), which is based on the matrix decomposition. The asymmetric cryptographic algorithm can effectively solve the robustness problem in WBANs. The implementation of semitensor-compressed sensing can encrypt multiple signals with different dimensions and reduce the amount of transmission. In addition, the hash function, Arnold scrambling, and chaotic scrambling are applied to improve the security of our algorithm. A series of simulation and security analysis, including key space, pixel distribution of the encrypted image, adjacent pixel correlation, required storage space, compression ratio, peak-signal-to-noise ratio, and so on, are given to show the better performance of our proposed scheme.