Related papers: MOR Cryptosystem and classical Chevalley groups in…
One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy problem): given two elements a, b of a group G and the…
Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…
Using computational methods, we complete the determination of the $3$-modular character table of the Chevalley group $F_4(2)$ and its covering group.
Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to…
Starting from the one-way group action framework of Brassard and Yung (Crypto '90), we revisit building cryptography based on group actions. Several previous candidates for one-way group actions no longer stand, due to progress both on…
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…
In this thesis, we study algebraic coding theory based McEliece-type cryptosystems over quasi-cyclic codes. The main goal of this thesis is to construct a cryptosystem that resists quantum Fourier sampling making it quantum secure. We…
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…
The notions of stable and Morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word-hyperbolic group. For a word-hyperbolic group $G$, Kapovich provided a partial algorithm which, on input a…
The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining…
In this work is proposed a method using orthogonal matrix transform properties to encrypt and decrypt a message. It will be showed how to use matrix functions to create complex encryptions. Because orthogonal matrix are always…
We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given a trajectory with a fixed number of collisions, the algorithm modifies both the waiting…
The reality of the difficulties in investigation of finite groups are considered. It is shown that the consideration of symmetry properties of the $k$-orbits that are obtained with an action of a finite group $F=(V,\cdot)$ on Cartesian…
An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
This paper presents theoretical analysis and software implementation for real harmonics analysis on the special orthogonal group. Noncommutative harmonic analysis for complex-valued functions on the special orthogonal group has been studied…
In this paper, an algorithm is aimed to make a cryptosystem for gray level images based on voice features, secret sharing scheme and electromagnetic rotor machine. Here, Shamir secret sharing (k n) threshold scheme is used to secure a key…
This paper is an attempt to build a new public-key cryptosystem; similar to the McEliece cryptosystem, using permutation error-correcting codes. We study a public-key cryptosystem built using two permutation error-correcting codes. We show…
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover,…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix…