相关论文: Equivalence Classes in AES -- Part 1

The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…

The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand,…

We study a family of equivalence relations on $S_n$, the group of permutations on $n$ letters, created in a manner similar to that of the Knuth relation and the forgotten relation. For our purposes, two permutations are in the same…

Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well…

In recent years, several methods have been proposed for explaining individual predictions of deep learning models, yet there has been little study of how to aggregate these predictions to explain how such models view classes as a whole in…

We introduce almost supplementary difference sets (ASDS). For odd $m$, certain ASDS in ${\mathbb Z}_m$ that have amicable incidence matrices are equivalent to quaternary sequences of odd length $m$ with optimal autocorrelation. As one…

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…

We make some beginning observations about the category $\mathbb{E}\mathrm{q}$ of equivalence relations on the set of natural numbers, where a morphism between two equivalence relations $R,S$ is a mapping from the set of $R$-equivalence…

The lock-free, ordered, linked list is an important, standard example of a concurrent data structure. An obvious, practical drawback of textbook implementations is that failed compare-and-swap (CAS) operations lead to retraversal of the…

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…

We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…

This paper provides four different architectures for encrypting and decrypting 128 bit information via the AES. The encryption algorithm includes the Key Expansion module which generates Key for all iterations on the fly, Double AEStwo-key…

The independence equivalence class of a graph $G$ is the set of graphs that have the same independence polynomial as $G$. Beaton, Brown and Cameron (arXiv:1810.05317) found the independence equivalence classes of even cycles, and raised the…

A significant source of errors in Automatic Speech Recognition (ASR) systems is due to pronunciation variations which occur in spontaneous and conversational speech. Usually ASR systems use a finite lexicon that provides one or more…

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the exampes the…

Bosonic encodings of quantum information offer hardware-efficient, noise-biased approaches to quantum error correction relative to qubit register encodings. Implementations have focused in particular on error correction of stored, idle…

Most machine learning models, especially artificial neural networks, require numerical, not categorical data. We briefly describe the advantages and disadvantages of common encoding schemes. For example, one-hot encoding is commonly used…

End-to-end modeling (E2E) of automatic speech recognition (ASR) blends all the components of a traditional speech recognition system into a unified model. Although it simplifies training and decoding pipelines, the unified model is hard to…

Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)-free posets and…

This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of…