Patent ID: 8259932

Claim:
A method, implemented by a computing device, the method comprising: under the control of one or more processors of the computing devices executing computer readable instructions: generating l-isogenous elliptic curves modulo p; computing a modular polynomial modulo a large prime p as a function of the l-isogenous elliptic curves wherein the computing comprises: interpolating information based on connectedness of a graph of the generated l-isogenous elliptic curves modulo p; determining a set of isogenies of degree l between supersingular elliptic curves modulo p; and for a given j-invariant of a supersingular elliptic curve over a finite field F p 2 , determining a univariate polynomial φ l (x, j) modulo p as a function of l+1 distinct subgroups of order l and j-invariants of l+1 corresponding l-isogenous elliptic curves of the set of isogenies; wherein l and p are distinct primes; and storing the modular polynomial to memory for utilization in a cryptosystem, for computational number theory, or in an elliptic curve point-counting algorithm.