Computerized method for signing a message
First Claim
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)=xk +ak-1 xk-1 + . . . +a1 x+a0, where the coefficients ak-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.
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Accused Products
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)=xk +ak-1 xk-1 + . . . +a1 x+a0, whose coefficients ak-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.
28 Citations
20 Claims
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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:
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forming a polynomial of the form P(x)=xk +ak-1 xk-1 + . . . +a1 x+a0, where the coefficients ak-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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 20)
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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:
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forming a polynomial of the forming P(x)=xk +ak-1 xk-1 + . . . +a1 x+a0, where the coefficients ak-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. - View Dependent Claims (11, 12, 13, 14, 15, 16, 17, 18, 19)
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Specification