Group signature generation system using multiple primes
First Claim
1. A method 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 the steps of;
a first individual in a group 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;
at least a second individual in said group performing a second partial digital signature subtask on said message M using a second individual private key to produce a second partial digital signature S2; and
combining said partial digital signature results including said results S1 and S2 to produce the group digital signature S corresponding to said message M.
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Abstract
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.
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Citations
19 Claims
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1. A method 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 the steps of;
a first individual in a group 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;
at least a second individual in said group performing a second partial digital signature subtask on said message M using a second individual private key to produce a second partial digital signature S2; and
combining said partial digital signature results including said results S1 and S2 to produce the group digital signature S corresponding to said message M. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 18, 19)
- M≦
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11. 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. - View Dependent Claims (13, 15)
- M≦
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16. 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.
- M≦
Specification