Results 251 to 260 of about 762,592 (290)

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.
Arne Winterhof
exaly   +4 more sources

Discrete Logarithm and Minimum Circuit Size

Information Processing Letters, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +5 more sources

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
openaire   +2 more sources

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
openaire   +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
openaire   +3 more sources

Discrete Logarithms: The Past and the Future

Designs, Codes and Cryptography, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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
openaire   +1 more source

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
openaire   +2 more sources

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
openaire   +1 more source

The Discrete-Logarithm Problem with Preprocessing

2018
This paper studies discrete-log algorithms that use preprocessing. In our model, an adversary may use a very large amount of precomputation to produce an “advice” string about a specific group (e.g., NIST P-256). In a subsequent online phase, the adversary’s task is to use the preprocessed advice to quickly compute discrete logarithms in the group ...
Henry Corrigan-Gibbs, Dmitry Kogan
openaire   +3 more sources