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· . . . ·pk, k is an integer greater than 2, and S≡Md(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.