Álvar Ibeas

Attacking the Pollard Generator

Let p be a prime and let c be an integer modulo p. The Pollard generator is a sequence (u_n) of pseudorandom numbers defined by the relation u_n+1equivu_n ²+c mod p. It is shown that if c and 9/14 of the most significant bits of two consecutive values u_n,u_n+1 of the Pollard generator are given, one can recover in polynomial time the initial value u₀ with a probabilistic algorithm. This result is an improvement of a theorem in a recent paper which requires that 2/3 of the most significant bits be known

Inferring sequences produced by a linear congruential generator on elliptic curves missing high-order bits

Let p be a prime and let

Cryptanalysis of the quadratic generator

E(\mathbb{F}_p)

On the linear complexity of the Naor–Reingold sequence

be an elliptic curve defined over the finite field

Recovering a sum of two squares decomposition

\mathbb{F}_p

Noisy Interpolation of Multivariate Sparse Polynomials in Finite Fields

of p elements. For a given point