Pla Information
Abstract
In this paper we combine the generalized Mersenne prime and the CM method to construct Montgomery-form elliptic curves, besides it sufficiently use pre-computation, compared with the former method, the new method not only improves the speed of selecting curves, but also improves the efficiency of the public key cryptosystems.
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In this paper we combine the generalized Mersenne prime and the CM method to construct Montgomery-form elliptic curves, besides it sufficiently use pre-computation, compared with the former method, the new method not only improves the speed of selecting curves, but also improves the efficiency of the public key cryptosystems.
Key concepts: Mersenne prime, Elliptic curve, Mathematics, Schoof's algorithm, Elliptic curve point multiplication, Prime (order theory), Hessian form of an elliptic curve, Edwards curve