Group signature generation system using multiple primes

摘要

A method is provided for generating a group digital signature wherein each of a group of individuals may sign a message M to create a group digital signature S, wherein M corresponds to a number representative of a message, 0<=M<=n-1, n is a composite number formed from the product of a number k of distinct random prime factors p₁.p₂. . . . .p_k, k is an integer greater than 2, and S≡M^d(mod n). The method may include: performing a first partial digital signature subtask on a message M using a first individual private key to produce a first partial digital signature S₁; performing at least a second partial digital signature subtask on the message M using a second individual private key to produce a second partial digital signature S₂; and combining the partial digital signature results to produce a group digital signature S.