Results 1 to 10 of about 1,067,462 (345)

Logarithm of the Discrete Fourier Transform [PDF]

International Journal of Mathematics and Mathematical Sciences, 2007
The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.
Michael Aristidou, Jason Hanson
doaj   +4 more sources

Quantum Circuit Optimization for Solving Discrete Logarithm of Binary Elliptic Curves Obeying the Nearest-Neighbor Constrained [PDF]

Entropy, 2022
In this paper, we consider the optimization of the quantum circuit for discrete logarithm of binary elliptic curves under a constrained connectivity, focusing on the resource expenditure and the optimal design for quantum operations such as the addition,
Jianmei Liu, Hong Wang, Zhi Ma, Qianheng Duan, Yangyang Fei, Xiangdong Meng   +5 more
doaj   +2 more sources

Mapping the Discrete Logarithm [PDF]

Involve, a Journal of Mathematics, 2006
The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional graph is largely dependent on an interaction between g and p-1.
Daniel R. Cloutier, Joshua Holden
openalex   +7 more sources

Quantum computation of discrete logarithms in semigroups [PDF]

Journal of Mathematical Cryptology, 2014
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines.
Childs Andrew M., Ivanyos Gábor
doaj   +6 more sources

Discrete Logarithm Factory

IACR Communications in Cryptology
The Number Field Sieve and its variants are the best algorithms to solve the discrete logarithm problem in finite fields (except for the weak small characteristic case).
Haetham Al Aswad, Cécile Pierrot, Emmanuel Thomé   +2 more
semanticscholar   +3 more sources

The Discrete Logarithm Problem [PDF]

Open Problems in Mathematics, 2016
For large prime numbers p, computing discrete logarithms of elements of the multiplicative group (Z∕pZ)∗ is at present a very difficult problem. The security of certain cryptosystems is based on the difficulty of this computation. In this expository paper we discuss several generalizations of the discrete logarithm problem and we describe various ...
René Schoof
semanticscholar   +4 more sources

A Plain-Image-Related Chaotic Image Encryption Algorithm Based on DNA Sequence Operation and Discrete Logarithm

IEEE Access, 2019
According to the research works of the literatures on chaotic cryptanalysis, many recent chaotic image encryption algorithms cannot resist chosen-plaintext attack.
Wei Feng, Yigang He, Hongmin Li, Chunlai Li   +3 more
doaj   +2 more sources

Asymmetric cipher protocol using conjugacy and discrete logarithm problem

Lietuvos Matematikos Rinkinys, 2009
The paper proposes asymmetric cipher protocol based on matrix field over some field F. The asymmetric cipher is based on two simultaneous problems: matrix conjugator search problem (MCSP) and matrix discrete logarithm problem (MDLP).
Andrius Raulynaitis, Agnė Venclovienė   +1 more
doaj   +3 more sources

A factoring and discrete logarithm based cryptosystem [PDF]

International Journal of Contemporary Mathematical Sciences, 2013
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Abdoul Aziz Ciss, Ahmed Youssef
openalex   +4 more sources

Fast parallel molecular algorithms for DNA-based computation: solving the elliptic curve discrete logarithm problem over GF2. [PDF]

J Biomed Biotechnol, 2008
Li K, Zou S, Xv J.
europepmc   +3 more sources