2014/03/12 by Abdoul Aziz Ciss, Ciss, Abdoul Aziz
Computer Science · #Chaos-based Image/Signal Encryption #Cryptography and Data Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #cs.CR
paper · pdf · doi:10.48550/arxiv.1404.2226
openalex publication_date 2014/03/12 · arxiv created 2014/08/25 · arxiv updated 2014/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the task of two-sources randomness extractors for elliptic curves defined over finite fields K, where K can be a prime or a binary field. In fact, we introduce new constructions of functions over elliptic curves which take in input two random points from two differents subgroups. In other words, for a ginven elliptic curve E defined over a finite field \mathbbFq and two random points P ∈ P and Q∈ Q, where P and Q are two subgroups of E(\mathbbFq), our function extracts the least significant bits of the abscissa of the point P⊕ Q when q is a large prime, and the k-first \mathbbFp coefficients of the asbcissa of the point P⊕ Q when q = pn, where p is a prime greater than 5. We show that the extracted bits are close to uniform. Our construction extends some interesting randomness extractors for elliptic curves, namely those defined in \citeop and \citeciss1,ciss2, when P = Q. The proposed constructions can be used in any cryptographic schemes which require extraction of random bits from two sources over elliptic curves, namely in key exchange protole, design of strong pseudo-random number generators, etc.