Method for determining the cofactor of an elliptic curve, corresponding electronic component and computer program product

摘要

A method and apparatus are proposed for cryptographic computations implemented in an electronic component. The method includes determining the cofactor of an elliptic curve E defined over a finite field Fq with q elements, the elliptic curve comprising a base point P having an order equal to n. The step of determining includes determining a value of floor((q+2ceil(b/2)+1+1)/n) when n>6√q, where the function ceil corresponds to the ceiling function, floor corresponds to the floor function, and b corresponds to the size q in number of bits of q.

主权项

1. A method for cryptographic computations implemented in an electronic component implemented within a first electronic device, wherein the method comprises:
determining a cofactor of an elliptic curve E defined over a finite field Fq with q elements using the electronic component that is configured to determine the cofactor, said elliptic curve comprising a base point P having an order equal to n, wherein determining the cofactor comprises determining a value of floor((q+2ceil(b/2)+1+1)/n) as the cofactor when n>6√q using the electronic component, where the function ceil corresponds to the ceiling function, floor corresponds to the floor function, and b corresponds to the size q in number of bits of q; performing, using the electronic component, a cryptographic function based on elliptic curve cryptography using the cofactor; and exchanging, by the first electronic device, data relating to said cryptographic function with a second electronic device.