A New Automatic Tool Searching for Impossible Differential of NIST Candidate ACE

The ACE algorithm is a candidate of the Lightweight Cryptography standardization process started by the National Institute of Standards and Technology (NIST) of the USA that passed the first round and successfully entered the second round. It is designed to achieve a balance between hardware cost and software efficiency for both authenticated encryption with associated data (AEAD) and hashing functionalities. This paper focuses on the impossible differential attack against the ACE permutation, which is the core component of the ACE algorithm. Based on the method of characteristic matrix, we build an automatic searching algorithm that can be used to search for structural impossible differentials and give the optimal permutation for ACE permutation and other SPN ciphers. We prove that there is no impossible differential of ACE permutation longer than 9 steps and construct two 8-step impossible differentials. In the end, we give the optimal word permutation against impossible differential cryptanalysis, which is π′=(2,4,1,0,3), and a safer word XOR structure of ACE permutation.

Reliability Optimization and Importance Analysis of Circular-Consecutive k-out-of-n System

The circular-consecutive k-out-of-n:F(G) system (Cir/Con/k/n:F(G) system) usually consists of n components arranged in a circle where the system fails (works) if consecutive k components fail (work). The optimization of the Cir/Con/k/n system is a typical case in the component assignment problem. In this paper, the Birnbaum importance-based genetic algorithm (BIGA), which takes the advantages of genetic algorithm and Birnbaum importance, is introduced to deal with the reliability optimization for Cir/Con/k/n system. The detailed process and property of BIGA are put forward at first. Then, some numerical experiments are implemented, whose results are compared with two classic Birnbaum importance-based search algorithms, to evaluate the effectiveness and efficiency of BIGA in Cir/Con/k/n system. Finally, three typical cases of Cir/Con/k/n systems are introduced to demonstrate the relationships among the component reliability, optimal permutation, and component importance.

Optimal recombination in genetic algorithms for combinatorial optimization problems: Part I

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results. Part I presents the basic principles of optimal recombination with a survey of results on Boolean Linear Programming Problems. Part II (to appear in a subsequent issue) is devoted to the ORPs for problems which are naturally formulated in terms of search for an optimal permutation.