1. A computer-implemented process for generating a curve for use in cryptography, comprising: selecting a suitable large prime number from a predefined set of large prime numbers; generating an Igusa class polynomial over the rational numbers from Igusa class polynomials modulo small primes; using the selected large prime number and the Igusa class polynomial over the rational numbers to compute a root of the Igusa class polynomial modulo the selected large prime number; using the computed root to generate a genus 2 curve; and using the genus curve for a cryptographic application.