Results 261 to 270 of about 3,524 (301)

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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Improvement of signature scheme based on factoring and discrete logarithms

Applied Mathematics and Computation, 2005
Laih and Kuo proposed two efficient signature schemes based on discrete logarithms and factorization. However, their schemes require many keys for a signing document.
Li-Hua Li, Shiang-Feng Tzeng
exaly   +1 more source

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: The Past and the Future

Designs, Codes and Cryptography, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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. Odlyzko, Richard Schroeppel   +2 more
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Discrete logarithms for finite groups

Computing, 2009
Let \(G\) be an arbitrary finite group, \({ \alpha}=( \alpha_{1}, \dots , \alpha_{t})\) an ordered \(t\)-tuple of elements of \(G\) such that \(G= \langle \alpha_{1}, \dots , \alpha_{t} \rangle\) and \[ S_{k}( \alpha)= \{ \prod_{i=1}^{k}( \alpha_{1}^{x_{i,1}} \cdots \alpha_{t}^{x_{i,t}}) \mid x_{i,j} \in { \mathbb Z}\}. \] Since \(G= \langle \alpha_{1},
Lee C. Klingler, Spyros S. Magliveras, Fred Richman, Michal Sramka   +3 more
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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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Test embedding with discrete logarithms

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1995
When using Built-In Self Test (BIST) for testing VLSI circuits, a major concern is the generation of proper test patterns that detect the faults of interest. Usually a linear feedback shift register (LFSR) is used to generate test patterns. We first analyze the probability that an arbitrary pseudo-random test sequence of short length detects all faults.
Mody Lempel, Sandeep K. Gupta 0001, Melvin A. Breuer   +2 more
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Fixed Points for Discrete Logarithms

2010
We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root g and an integer x in the interval [1,p − 1] with log g x = x. Here, log g is the discrete logarithm function to the base g for the cyclic group (ℤ/pℤ)×. Tools include a numerically explicit “smoothed” version of the Polya–Vinogradov inequality for the sum of ...
Mariana Levin, Carl Pomerance, K. Soundararajan   +2 more
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Interpolation of the Double Discrete Logarithm

2008
The double discrete logarithm has attracted interest as a one-way function in cryptography, in particular in group signature schemes and publicly verifiable secret sharing schemes. We obtain lower bounds on the degrees of polynomials interpolating the double discrete logarithm in multiplicative subgroups of a finite field and in the group of points on ...
Gerasimos C. Meletiou, Arne Winterhof
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