As a core component of Substitution-Permutation Networks, diffusion layer is mainly introduced by matrices from maximum distance separable (MDS) codes. Surprisingly, up to now, most constructions of MDS matrices require to perform an equivalent or even exhaustive search. Especially, not many MDS proposals are known that obtain an excellent hardware efficiency and simultaneously guarantee a rema...

We present a new garbled circuit construction for two-party secure function evaluation (SFE). In our one-round protocol, XOR gates are evaluated “for free”, which results in the corresponding improvement over the best garbled circuit implementations (e.g. Fairplay [19]). We build permutation networks [26] and Universal Circuits (UC) [25] almost exclusively of XOR gates; this results in a factor...

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circul...

The main contribution of this paper is to introduce an autonomous definition of the connective “fuzzy exclusive or” (fuzzy Xor, for short), which is independent from others connectives. Also, two canonical definitions of the connective Xor are obtained from the composition of fuzzy connectives, and based on the commutative and associative properties related to the notions of triangular norms, t...

Settling a conjecture of Shi and Zhang [ZS09], we determine the unbounded-error communication complexity of the symmetric XOR functions up to a poly-logarithmic factor. Our proof is by a simple reduction to an earlier result of Sherstov.

Transient simulation of a gate circuit is an efficient method of counting signal changes occurring during a transition of the circuit. It is known that this simulation covers the results of classical binary analysis, in the sense that all signal changes appearing in binary analysis are also predicted by the simulation. For feedback-free circuits of 1and 2-input gates, it had been shown that the...

Three-level logic is shown to have a potential for reduction of the area over two-level implementations, as well as for a gain in speed over multi-level implementations. Algorithms for finding AND-OR-XOR and AND-OR-AND expressions were developed, however an open problem remained which of the algorithms should be used to find an optimal solution for a given function. In this paper we formulate a...

We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field GF(2), which is most naturally considered as a projective transformation. Such a viewpoint allows us to demonstrate certain properties of this AES nonlinear function. In particular, we make some comments about the group generated by such transfo...

CVT and XOR are two binary operations together used to calculate the sum of two non-negative integers on using a recursive mechanism. In this present study the convergence behaviors of this recursive mechanism has been captured through a tree like structure named as CVT-XOR Tree. We have analyzed how to identify the parent nodes, leaf nodes and internal nodes in the CVT-XOR Tree. We also provid...

The perfect phylogeny model for haplotype evolution has been successfully applied to haplotype resolution from genotype data. In this study we explore the application of the perfect phylogeny model to other problems in the design and analysis of genetic studies. We consider a novel type of data, xor-genotypes, which distinguish heterozygote from homozygote sites but do not identify the homozygo...