Patent ID: 7215780

Claim:
A method of providing a point multiple in an elliptic curve cryptosystem for performing cryptographic operations, said point multiple being derived from a scalar and a point on an elliptic curve having an equation of the form y 2 +xy=x 3 +a 1 x 2 +1, where a 1 is either 0 or 1, said method comprising the steps of a) obtaining a pair of coefficients derived from a truncator of said elliptic curve; b) computing a representation of said scalar from said pair of coefficients, said scalar, and said truncator of said elliptic curve; c) computing said point multiple using said representation of said scalar and a Frobenius mapping τ; and d) providing said point multiple to said elliptic curve cryptosystem for use in said cryptographic operations; wherein said truncator is τ m - 1 τ - 1 , and wherein m is the extension degree of a finite field over which said elliptic curve is defined.