Patent ID: 8014521

Claim:
A method of operating a cryptographic system including instructions, the method comprising: (a) causing a base point generator to generate a divisor of a hyperelliptic curve of genus 2 in characteristic 2, the hyperelliptic curve being defined by y 2 +h(x)y=f(x), the divisor being equal to a formal sum of points, wherein: (a) y is a first point on the hyperelliptic curve; (b) x is a second point on the hyperelliptic curve; (c) h(x) is a first polynomial; and (d) f(x) is a second polynomial; (b) causing a processor to execute the instructions to cause the processor to perform halving on the generated divisor of the hyperelliptic curve of genus 2 in characteristic 2; and (c) causing the processor to execute the instructions to cause the processor to perform scalar multiplication using the halved divisor of the hyperelliptic curve of genus 2 in characteristic 2.