Efficient Multiplication in for Elliptic Curve Cryptography
Jean-Claude Bajard, Laurent Imbert, Christophe Négre, Thomas Plantard · 2003
We present a new multiplication algorithm for the implementation of elliptic curve cryptography (ECC) over the finite extension ���������� � fields � where is a prime number greater �� � than. In the context of ECC we can assume � that is �-to-�¦ � a-bit number, and easily find values � for which ������ � satisfy: , and for security reasons within an alternate polynomial representation of the field elements which is directly obtained from the inputs. No conversion step is needed. We describe our algorithm in terms of matrix operations and point out some properties of the matrices that can be used to improve the design. The proposed algorithm is highly parallelizable and seems well adapted to hardware implementation of elliptic curve cryptosystems. ���������������� �. All the computations are performed