Cryptographic computation method, cryptographic system, and computer program

A cryptographic system comprising:

• a processor;
• a base point generator operatively connected to the processor, the base point generator which generates a divisor of a hyperelliptic curve of genus 2 in characteristic 2, the hyperelliptic curve being defined by y2+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;
• and
• a memory device operatively coupled to the processor, the memory device storing instructions which when executed by the processor, cause the processor, in cooperation with the memory device to:
• (a) perform halving on the generated divisor of the hyperelliptic curve of genus 2 in characteristic 2;
• and
• (b) perform scalar multiplication using the halved divisor of the hyperelliptic curve of genus 2 in characteristic 2.

A non-transitory computer-readable medium storing instructions structured to cause a computer to:

• (a) generate a divisor of a hyperelliptic curve of genus 2 in characteristic 2, the hyperelliptic curve being defined by y2+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;
• and
• (b) perform halving on the generated divisor of the hyperelliptic curve of genus 2 in characteristic 2;
• and
• (c) perform scalar multiplication using the halved divisor of the hyperelliptic curve of genus 2 in characteristic 2.