Results 291 to 300 of about 1,067,462 (345)

Discrete logarithms inGF(p)

Algorithmica, 1986
Several related algorithms are presented for computing logarithms in fieldsGF(p),p a prime. Heuristic arguments predict a running time of exp((1+o(1)) $$\sqrt {\log p \log \log p} $$ ) for the initial precomputation phase that is needed for eachp, and much ...
Andrew Odlyzko, Richard Schroeppel, Don Coppersmith   +2 more
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The One-More Discrete Logarithm Assumption in the Generic Group Model

IACR Cryptology ePrint Archive, 2021
B. Bauer, Georg Fuchsbauer, Antoine Plouviez   +2 more
semanticscholar   +1 more source

Discrete Logarithms and Diffie–Hellman

2014
In 1976, Whitfield Diffie and Martin Hellman published their now famous paper [38] entitled “New Directions in Cryptography.” In this paper they formulated the concept of a public key encryption system and made several groundbreaking contributions to this new field.
Jill Pipher, Joseph H. Silverman, Jeffrey Hoffstein   +2 more
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Quantum Cryptanalysis Landscape of Shor's Algorithm for Elliptic Curve Discrete Logarithm Problem

Web Information System and Application Conference, 2021
Harashta Tatimma Larasati, Howon Kim
semanticscholar   +1 more source

Discrete Logarithms: Recent Progress

2000
We summarize recent developments on the computation of discrete logarithms in general groups as well as in some specialized settings. More specifically, we consider the following abelian groups: the multiplicative group of finite fields, the group of points of an elliptic curve over a finite field, and the class group of quadratic number fields.
Johannes Buchmann, Damian Weber
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The Discrete Logarithm Problem

1999
The public key cryptosystems presented in Chapter 1 rely on the difficulty of solving the discrete logarithm problem in certain groups: An adversary who could efficiently compute discrete logarithms in the group underlying such a cryptosystem would be able to break the system. So to judge the security of the proposed cryptosystems we must have a closer
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Linear complexity of the discrete logarithm

Designs, Codes and Cryptography, 2003
We obtain new lower bounds on the linear complexity of several consecutive values of the discrete logarithm modulo a prime p. These bounds generalize and improve several previous results.
Igor E. Shparlinski, Sergei Konyagin, Tanja Lange   +2 more
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Quantum algorithm for solving hyperelliptic curve discrete logarithm problem

Quantum Information Processing, 2020
Yan Huang, Zhaofeng Su, Fangguo Zhang, Yong Ding, Rong Cheng   +4 more
semanticscholar   +1 more source

Low Weight Discrete Logarithm and Subset Sum in 20.65n with Polynomial Memory

International Conference on the Theory and Application of Cryptographic Techniques, 2020
Andre Esser, Alexander May
semanticscholar   +1 more source

The Multi-Base Discrete Logarithm Problem: Tight Reductions and Non-rewinding Proofs for Schnorr Identification and Signatures

International Conference on Cryptology in India, 2020
M. Bellare, Wei Dai
semanticscholar   +1 more source