Group signature generation system using multiple primes

A method of creating and assigning individual private keys to each member of at least one group of individuals, wherein the individuals in each group may, use their assigned keys to sign a message M to collectively create a group digital signature S associated with an entity that includes all of the groups, 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 total number k of distinct random primes p1·p2· . . . ·pk, k is an integer greater than 2, and S≡Md(mod n), and wherein each such group of individuals collectively control all of the primes, but wherein no single one of the individuals controls all of the prime factors p1, p2, . . . pk, comprising:

• assigning at least one of the total number k of prime numbers p1, p2, . . . pk to each of a plurality of members of each of at least one group, wherein all of the prime numbers assigned to the individuals within each group are distinct;
• defining a unique individual modulus associated with each of the individuals formed as the product of the prime numbers assigned to the individual;
• and
• defining a unique individual private key for each of the individuals based on the associated individual modulus formed for the individual;
• whereby each of the individual private keys may be used to create an associated individual partial digital signature, wherein the individual partial digital signatures of the members of a group may be combined to form the group digital signature S, and wherein at least one of the partial digital signatures cannot be combined across different groups to form the group digital signature S.

An apparatus 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), comprising:

• a secure key generation facility;
• a plurality of individual secure private key storage and signing entities;
• and
• a secure group signature combining entity.