2010/05/21 by Chantal David, Jie Wu, David, Chantal +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1005.3871
arxiv created 2010/05/21 · openalex publication_date 2010/05/21 · arxiv updated 2010/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E be an elliptic curve over \Fp without complex multiplication, and for each prime p of good reduction, let nE(p) = | E(\Fp) |. Let QE,b(x) be the number of primes p ≤ x such that bnE(p) ≡ b (\rm mod nE(p)), and πE, b\rm pseu(x) be the number of \it compositive nE(p) such that bnE(p) ≡ b (\rm mod nE(p)) (also called elliptic curve pseudoprimes). Motivated by cryptography applications, we address in this paper the problem of finding upper bounds for QE,b(x) and πE, b\rm pseu(x), generalising some of the literature for the classical pseudoprimes \citeErdos56, Pomerance81 to this new setting.