Under the quadratic-residuosity assumption, we show that the function that maps the pair to the Legendre sequence of modulo , with respect to public random offsets , is a pseudorandom generator. This answers an open question of Damgård (CRYPTO 1988), up to the choice of the offsets .
Aug 9, 2024
Under the quadratic-residuosity assumption, we show that the function that maps the pair (x, p) to the Legendre sequence of x modulo p, with respect to public ...
The Legendre sequence of an integer x modulo a prime p with respect to offsets ⃗a = ( a 1 , . . . , a ℓ ) is the string of Legendre symbols ( x + a 1 p ) ...
Legendre Sequences are Pseudorandom under the Quadratic-Residuosity Assumption. Henry Corrigan-Gibbs and David J. Wu. Resources. Paper: [PDF], [ePrint Version].
Under the quadratic-residuosity assumption, we show that the function that maps the pair (x,p) ( x , p ) to the Legendre sequence of x x modulo p p , with ...
Legendre Sequences are Pseudorandom under the Quadratic-Residuosity Assumption. The Legendre sequence of an integer $x$ modulo a prime $p$ with respect to ...
Mar 1, 2023 · Sequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988.
In a stream cipher the sequence K, however, is a pseudorandom sequence, which is a sequence of numbers (or of bits) that appears to be “random” yet repeatable.
Damgård has proposed another method to obtain pseudo-random binary sequences, namely by using Legendre and Jacobi sequences [10]. These are simply obtained by ...
A number r is called a quadratic residue modulo N if there exist a number x such that x2 ≡ r (mod N).