IDENTITY BASED ELLIPTIC CURVE CRYPTOGRAPHY

摘要

Method includes ascertaining a friendly prime (p) based on a first variable (c) and Nth power of two, N being an integer and the c selected using log2c=(1/2)N. p is congruent to 3(mod 4) and has 512 bit length. Generating, based on distinctive parameters, a super singular elliptic curve (E/GF(p)) over a finite field (GF(p)). A first torsion group (S[q]) over the E/GF(p) is determined based on the p, the S[q] being a subgroup of points over the E/GF(p). A torsion group prime order (q) of the S[q] is a prime number of 160 bit length.Constructing a second torsion group T[q], an isomorphic image of the S[q], over a super singular elliptic curve (E/GF(p2)) based on the p. A (q) of the T[q] is equal to the (q) of the S[q]. The (p), the (E/GF(p)), the S[q], and the T[q], are provided to a user device.