Abstract The present invention improves speed and reduces complexity in a digital signature scheme that uses elliptic algebra. The signature scheme generates two points that are compared. If the points do not match, the signature is not authentic. The present invention reduces computations by comparing only the x coordinates of the two generated points. The invention provides a scheme for deducing the possible values of the x-coordinate of a sum of two points using only the x coordinates of the original two points in question. The present invention provides a scheme that limits the possible solutions that satisfy the equation to two (the authentic signature and one other). Because of the large number of possible inauthentic solutions, the chance of a false authentic signature is statistically insignificant.
A method for creating and authenticating a digital signature comprising the steps of: in a sender computer system; generating a random integer m; using m, generating a point P 1 having coordinates (X 1 , Y 1 ); using m and P 1 , generating a point u; sending the pair (u, P 1 ) as a digital signature to a receiver computer system; in said reciever computer system; using u, generating a point Q having coordinates (X, Y); using P 1 , generating a point P 2 having coordinates (X 2 , Y 2 ); without using Y 1 and Y 2 , testing the equality P 1 +P 2 =Q; identifying a signature as not authentic when the equality P 1 +P 2 =Q is not satisfied.
Claim 2
Independent Claim
129 words
A method for creating and authenticating a digital signature comprising the steps of: in a sender computer system; generating a random integer m; using m, generating a point P 1 having coordinates (X 1 , Y 1 ); using m and P 1 , generating a point u; sending the pair (u, P 1 ) as a digital signature to a receiver computer system; in said reciever computer system; using u, generating a point Q having coordinates (X, Y); using P 1 , generating a point P 2 having coordinates (X 2 , Y 2 ); without using Y 1 and Y 2 , testing the equality P 1 +P 2 =Q; identifying a signature as not authentic when the equality P 1 +P 2 =Q is not satisfied.