Pseudoprime Reductions of Elliptic Curves
نویسندگان
چکیده
Let E be an elliptic curve over Q without complex multiplication, and for each prime p of good reduction, let nE(p) = |E(Fp)|. For any integer b, we are studying in this paper elliptic pseudoprimes to the base b. More precisely, let QE,b(x) be the number of primes p 6 x such that bE ≡ b (modnE(p)), and π E,b (x) be the number of compositive nE(p) such that b nE(p) ≡ b (modnE(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 π E,b (x), generalising some of the literature for the classical pseudoprimes [6, 17] to this new setting.
منابع مشابه
Pseudoprime reductions of elliptic curves
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