Scalar point multiplication using redundant recoding in elliptic curve cryptosystems
Sangook Moon · 2005
Scalar multiplication is the backbone operation in elliptic curve cryptosystems, and its implementation algorithms are expected to exhibit high performance. We introduce a point quadruple scalar operation in an elliptic curve cryptosystem to be used in a novel scalar point multiplication algorithm, named quad-and-add. Expressions derived by the algorithm were applied to a real prototype cryptosystem and evaluated at both C language and HDL level. Point quadruple operation with the proposed quad-and-add algorithm were twice as fast as the traditional double-and-add algorithm when we fixed the radix number at four.