Results 181 to 190 of about 169,709 (230)

The Discrete Logarithm Problem

1993
There are many public-key cryptosystems whose security lies in the presumed intractability of the discrete logarithm problem in some group G. The discrete logarithm problem has received a great deal of attention in recent years, and numerous algorithms which use a variety of techniques have been devised.
Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian   +4 more
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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 ...
Don Coppersmith, Andrew M. Odlzyko, Richard Schroeppel   +2 more
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Kangaroos, Monopoly and Discrete Logarithms

Journal of Cryptology, 2000
The Pollard ``rho'' and ``kangaroo'' methods for finding the discrete logarithm in any cyclic group are discussed. For the rho method, the order of the group, \(g\), must be known and it runs in \(O(q^{1/2})\) time where \(q\) is the largest prime divisor of \(g\). For the kangaroo method, it is not necessary to know \(g\) but only that it lies in some
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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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Linear Complexity of the Discrete Logarithm

Designs, Codes and Cryptography, 2003
The authors prove several lower bounds on the linear complexity of finite sequences consisting of consecutive values of the discrete logarithm modulo a prime. The method and the results are new and deserve highest notice in mathematical cryptography. In particular, several previously known results are improved.
Konyagin, S., Lange, T., Shparlinski, I.E.   +2 more
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Discrete Logarithm Problems with Auxiliary Inputs

Journal of Cryptology, 2009
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Polynomial Interpolation of the Discrete Logarithm

Designs, Codes and Cryptography, 2002
The paper provides lower bounds on the degree and the sparsity of polynomials interpolating the discrete logarithm in a finite field. The results extend the work of \textit{D. Coppersmith} and \textit{I. E. Shparlinski} [J. Cryptology 13, 339-360 (2000; Zbl 1038.94007)] from finite prime fields to arbitrary finite fields.
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Discrete Logarithm and Minimum Circuit Size

Information Processing Letters, 2017
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