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Fast Divisor Scalar Multiplications on a Class of Hyperelliptic Curves

Lin You

Open publisher page 1 citations

Abstract

Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem.Based on the idea of simple divisor scalar multiplications,Duursma and Sakurai's algorithm for divisor scalar multiplications on a special class of hyperelliptic curves over prime fields has been improved to a larger class of such hyperelliptic curves over prime-extension fields,and two new formulized algorithms for divisor scalar multiplications are proposed.Compared with binary method,our algorithms are much more efficient and take at least 12% less computation amount.

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What this paper is about

Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem.Based on the idea of simple divisor scalar multiplications,Duursma and Sakurai's algorithm for divisor scalar multiplications on a special class of hyperelliptic curves over prime fields has been improved to a larger class of such hyperelliptic curves over prime-extension fields,and two new formulized algorithms for divisor scalar multiplications are proposed.Compared with binary method,our algorithms are much more efficient and take at least 12% less computation amount.

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Available abstract

Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem.Based on the idea of simple divisor scalar multiplications,Duursma and Sakurai's algorithm for divisor scalar multiplications on a special class of hyperelliptic curves over prime fields has been improved to a larger class of such hyperelliptic curves over prime-extension fields,and two new formulized algorithms for divisor scalar multiplications are proposed.Compared with binary method,our algorithms are much more efficient and take at least 12% less computation amount.

Key concepts: Scalar multiplication, Mathematics, Hyperelliptic curve, Divisor (algebraic geometry), Hyperelliptic curve cryptography, Scalar (mathematics), Computation, Prime (order theory)

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