System and method for regenerating secret keys in diffie-hellman communication sessions
First Claim
1. A method for regenerating for a third party L a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties J, comprising the steps of:
- (1) providing a private value Xi of said first party I to said third party L;
(2) using a number n, the number n differing for each of said communication sessions, and said private value Xi, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p, wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions; and
(3) determining for said third party L a number m associated with said number n to regenerate said secret key Ks in a second modular exponentiation equation, whereby said third party is able to decipher each of said communication sessions.
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Abstract
The present invention is directed to a system and method for regenerating secret keys by escrowing only one private value in a Diffie-Hellman exchange where a public number is exchanged between the two participants according to the equation:
Y=g.sup.X mod p,
where Y is the Diffie-Hellman public number, X is the Diffie-Hellman private number, g is the generator, and p is the prime. The public value for each communication session is controlled after the escrow of the private value, and the secret keys are regenerated from the escrowed private value and the controlled public values. The escrowed private value is transmitted to the escrow center with full proof of security and authenticity and, if desired, this private value can be changed and re-sent to the escrow center.
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Citations
31 Claims
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1. A method for regenerating for a third party L a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties J, comprising the steps of:
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(1) providing a private value Xi of said first party I to said third party L; (2) using a number n, the number n differing for each of said communication sessions, and said private value Xi, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p,wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions; and(3) determining for said third party L a number m associated with said number n to regenerate said secret key Ks in a second modular exponentiation equation, whereby said third party is able to decipher each of said communication sessions. - View Dependent Claims (2, 3, 4, 5, 6, 7, 20, 21, 22)
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8. An apparatus for regenerating for a third party L a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties I, comprising:
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means for providing a private value Xi of said first party I to said third party L; means for using a number n, the number n differing for each of said communication sessions, and said private value Xi, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p,wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions; andmeans for determining for said third party L a number m associated with said number n to regenerate said secret key Ks in a second modular exponentiation equation, whereby said third party is able to decipher each of said communication sessions. - View Dependent Claims (9, 10, 11, 12, 23, 24, 25)
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13. A computer-readable medium embodying instructions for causing a device to generate a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties J, by the steps of:
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(1) providing a private value Xi of said first party I to a third party L; (2) using a number n, the number n differing for each of said communication sessions, and said private value Xi, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p,wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions; and(3) determining for said third party L a number m associated with said number n to regenerate said secret key Ks in a second modular exponentiation equation, whereby said third party L is able to decipher each of said communication sessions. - View Dependent Claims (14, 15, 16, 17, 18, 19, 26, 27, 28)
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29. A method for regenerating for a third party L a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties J, comprising the step of:
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using a number n at node A, the number n differing for each of said communication sessions, and a private value Xi of said first party I, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p,wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions;whereby a number m associated with said number n is determinable for a third party L to regenerate said secret key Ks in a second modular exponentiation equation and decipher each of said communication sessions.
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30. An apparatus for regenerating for a third party L a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties J, comprising:
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means for using a number n, the number n differing for each of said communication sessions, and a private value Xi of said first party I, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p,wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions;whereby a number m associated with said number n is determinable for a third party L to regenerate said secret key Ks in a second modular exponentiation equation and decipher each of said communication sessions.
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31. A computer-readable medium embodying instructions for causing a device to generate a secret key Ks used in a Diffie-Hellman communication session S among a plurality of sessions communicated between a first party I and one or more second parties J, by the steps of:
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using a number n, the number n differing for each of said communication sessions, and a private value Xi of said first party I, in a first modular exponentiation equation
space="preserve" listing-type="equation">Yi=g.sup.(Xi+n) mod p,wherein g represents a generator number and p represents a prime number, to generate a plurality of public values Yi of said first party I;
each of said public values Yi being associated with one public value Yj of said party J for each of said communication sessions;whereby a number m associated with said number n is determinable for a third party L to regenerate said secret key Ks in a second modular exponentiation equation and decipher each of said communication sessions.
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Specification