Computerized method for signing a message

• US 5,787,178 A
• Filed: 04/12/1996
• Issued: 07/28/1998
• Est. Priority Date: 04/12/1995
• Status: Expired due to Term

• Current Assignee: Deutsche Telekom AG
• Original Assignee: Deutsche Telekom AG
• Inventors: Schwenk, Joerg
• Primary Examiner(s): Tarcza, Thomas H.
• Assistant Examiner(s): White, Carmen D.
• Application Number:
  US08/631,278
• Time in Patent Office: 837 Days
• Field of Search: 380/30, 380/23, 380/25, 380/28
• US Class Current: 380/30
• CPC Class Codes: H04L 2209/26 Testing cryptographic entity, e.g. testing integrity of encryption key or encryption algorithm
• CPC Class Codes: H04L 9/3026 details relating to polynomials generation, e.g. generation of irreducible polynomials
• CPC Class Codes: H04L 9/3247 involving digital signatures

Abstract

A computerized method for signing a message, where a secret key is used for signing and the signature can be tested with the help of a public key, provides for the public key to be a number n that is the product of two large prime numbers p and q; the secret key includes at least one of the two prime numbers; a polynomial is created in the form P(x)=x^k +a_k-1 x^k-1 + . . . +a₁ x+a₀, whose coefficients a_k-1 . . . a₀ are formed from the message, taking into account a random number. This polynomial is used to derive additional polynomials P(x) mod p and P(x) mod q whose zeros in the respective finite fields GF(p) and GF(q) are defined. The zeros are combined into one or more solutions z of the equation P(x) mod n=0, and the random number and the solution z or selected solutions z are added as the signature to the message.

Claims

1. A method generating a digital signature and using the Signature to sign an electronic message, wherein a microprocessor uses a secret key for signing and the signature can be tested by an other microprocessor with the help of a public key, the public key being a number n that is the product of two prime numbers p and q, and the secret key including at least one of the two prime numbers p and q, the method comprising the steps of:

forming a polynomial of the form P(x)=x^k +a_k-1 x^k-1 + . . . +a₁ x+a₀, where the coefficients a_k-1 . . . a₀ are formed from the message by taking into account a random number,

deriving additional polynomials P(x) mod p and P(x) mod q;

determining, zeros in respective finite fields GF(p) and GF(q) of the additional polynomials P(x) mod p and P(x) mod q;

finding at least one solution z of the equation P(x) mod n=0 by using the zeros; and

joining the random number and the at least one solution z to the message.

2. The method as recited in claim 1 wherein the steps of forming the polynomial, deriving the additional polynomials and determining the zeros of the additional polynomials are repeated if necessary with another random number until each additional polynomial has at least one zero in its respective finite field.

3. The method as recited in claim 1 wherein the steps of creating the polynomial, deriving the additional polynomials and determining the zeros of the additional polynomials are repeated if necessary with another random number until both additional polynomials have at least a predetermined number of zeros in the respective finite field.

4. The method as recited in claim 1 wherein the solution z is calculated from the zeros of the additional polynomials by using an extended Euclidean algorithm and the Chinese Remainder theorem.

5. The method as recited in claim 1 wherein k>

2.

6. The method as recited in claim 1 wherein log₂ n≈

500.

7. The method as recited in claim 1 further comprising the step of verifying the signed message by determining whether the at least one solution z satisfies the equation P(z) mod n=0.

8. The method as recited in claim 1 further comprising the step of storing a list of public keys in the other microprocessor.

9. The method as recited in claim 1 further comprising the steps of storing at least one secret key in the microprocessor and accessing the secret key by entering a password.

20. The method as recited in claim 1 further comprising the step of transmitting the message and at least one solution z from the microprocessor to the other microprocessor.

10. A method for generating a digital signature and using the signature to sign an electronic message, wherein a microprocessor uses a secret key for signing and the signature can be tested by an other microprocessor with the help of a public key, the public key being a number n that is the product of two prime numbers p and q, and the secret key including at least one of the two prime numbers p and q, the method comprising the steps of:

forming a polynomial of the forming P(x)=x^k +a_k-1 x^k-1 + . . . +a₁ x+a₀, where the coefficients a_k-1 . . . a₀ are formed from the message and the coefficient a₀ is a random number,

deriving additional polynomials P(x) mod p and P(x) mod q;

determining zeros in respective finite fields GF(p) and GF(q) of the polynomials P(x) mod p and P(x) mod q;

finding at least one solution z of the equation P(x) mod n=0 by using the zeros; and

joining the random number and the at least one solution z to the message.

11. The method as recited in claim 10 wherein the message is divided into blocks forming the individual coefficients a_k-1 . . . a₁.

12. The method as recited in claim 10 wherein the steps of forming the polynomial, deriving the additional polynomials and determining the zeros of the additional polynomials are repeated if necessary with another random number until each additional polynomial has at least one zero in its respective finite field.

13. The method as recited in claim 10 wherein the steps of creating the polynomial, deriving the additional polynomials and determining the zeros of the additional polynomials are repeated if necessary with another random number until both additional polynomials have at least a predetermined number of zeros in the respective finite field.

14. The method as recited in claim 10 wherein the solution z is calculated from the zeros of the additional polynomials by using an extended Euclidean algorithm and the Chinese Remainder theorem.

15. The method as recited in claim 10 wherein k≧

2.

16. The method as recited in claim 10 wherein log₂ n≈

500.

17. The method as recited in claim 10 further comprising the step of verify in the signed message by determining whether the at least one solution z satisfies the equation P(z) mod n=0.

18. The method as recited in claim 10 further comprising the step of storing a list of public keys in the other microprocessor.

19. The method as recited in claim 10 further comprising the steps of storing at least one secret key in the microprocessor and accessing the secret key by entering a password.