Patent ID: 8817977

Claim:
A computer-implemented method comprising: generating a digital signature using an established elliptic curve having an order, the generating being performed under control of one or more computer systems configured with executable instructions and having an associated secret encryption key, and including: calculating a first magnitude representative of an inverse of a random number raised at least to the power two; obtaining a first element of a digital signature by executing a scalar multiplication between an established point of the established elliptic curve and the random number; obtaining a second magnitude by executing a modular multiplication, with modulus corresponding to the order of the established elliptic curve, between the first magnitude and one of the secret encryption key and the first element of the digital signature; obtaining a third magnitude by executing a modular multiplication, with modulus corresponding to the order of the established elliptic curve order, between the random number and one of the secret encryption key and the first element of the digital signature; obtaining a first addend by executing a modular multiplication, with modulus corresponding to the order of the established elliptic curve, between the second magnitude and the third magnitude; and generating a second element of the digital signature based at least in part on the first addend.