On the linear complexity and multidimensional distribution of congruential generators over elliptic curves

DOI10.1007/s10623-003-6153-0zbMath1116.14307OpenAlexW2018624813MaRDI QIDQ2572963

Igor E. Shparlinski, Florian Hess

Publication date: 7 November 2005

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-003-6153-0

zbMATH Keywords

exponential sumselliptic curvespseudorandom number generators

Mathematics Subject Classification ID

Elliptic curves (14H52) Exponential sums (11T23) Random number generation in numerical analysis (65C10)

Related Items (21)

Predicting the elliptic curve congruential generator ⋮ Linear complexity of some sequences derived from hyperelliptic curves of genus 2 ⋮ Binary sequences from a pair of elliptic curves ⋮ On the linear complexity profile of some sequences derived from elliptic curves ⋮ Inferring sequences produced by elliptic curve generators using Coppersmith's methods ⋮ Attacking the linear congruential generator on elliptic curves via lattice techniques ⋮ Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves ⋮ On the distribution of pseudorandom vectors generated by elliptic curves ⋮ ON THE -ERROR LINEAR COMPLEXITY OF SEQUENCES FROM FUNCTION FIELDS ⋮ An improved method for predicting truncated multiple recursive generators with unknown parameters ⋮ Elliptic curve analogue of Legendre sequences ⋮ On lattice profile of the elliptic curve linear congruential generators ⋮ On the elliptic curve endomorphism generator ⋮ Predicting nonlinear pseudorandom number generators ⋮ Pseudo-Randomness of Discrete-Log Sequences from Elliptic Curves ⋮ Distribution of some sequences of points on elliptic curves ⋮ A family of elliptic curve pseudorandom binary sequences ⋮ Extractors for binary elliptic curves ⋮ Inferring sequences produced by a linear congruential generator on elliptic curves missing high-order bits ⋮ Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith’s Methods ⋮ Pseudorandom vector generation using elliptic curves and applications to Wiener processes

Cites Work

• Lattice reduction: a toolbox for the cryptoanalyst
• Cyclicity statistics for elliptic curves over finite fields
• Linear complexity profiles: Hausdorff dimensions for almost perfect profiles and measures for general profiles
• On the Naor-Reingold pseudo-random function from elliptic curves
• On the cyclicity of elliptic curves over finite field extensions
• Reconstructing Truncated Integer Variables Satisfying Linear Congruences
• How to predict congruential generators
• Quasi-Monte Carlo methods and pseudo-random numbers
• On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves.
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the linear complexity and multidimensional distribution of congruential generators over elliptic curves