Patent ID: 7587605

Claim:
A computer-readable storage medium having computer-executable instructions that, when executed, direct a computer to perform a method comprising: obtaining a message M; defining a vector v to be v 1 , . . . , v n based upon a predefined first hashing function of the message M; calculating a private key α in accordance with this equation α = ∑ i = 1 n ⁢ ⁢ v i ⁢ α i ⁢ mod ⁢ ⁢ m , where m is an order of torsion points, α i are scaling factors in Q i =α i P (1≦i≦n), and P and Q i are elliptical curve points; producing a signature S in accordance with this equation: S=αH 2 (M), where H 2 (M) is a predefined second hashing function of the message M, wherein the predefined first hashing function differs from the predefined second hashing function and wherein the signature S is represented by a number of bits; truncating a specific number of bits off of signature S; after the truncating, indicating a message-and-signature pair (M, S) based, at least in part, on the obtaining, defining, calculating, or producing.