Fast Scalar Multiplication on the Jacobian of a Family of Hyperelliptic Curves
نویسندگان
چکیده
Hyperelliptic curve cryptosystems HCC for short is a gen eralization of ECC It has been drawing the attention of more and more researchers in recent years The problem of how to decrease the amount of addition and scalar multiplication on the Jacobians of hyperelliptic curves so that the implementation speed can be improved is very im portant for the practical use of HCC In this paper Using Frobenius endomorphism as a tool we discuss the problem of faster scalar mul tiplication A faster algorithm on Jacobian s scalar multiplication of a family of speci c hyperelliptic curves is proposed with its computational cost analyzed Analysis reveals that our algorithms s computational cost is less than that of Signed Binary Method
منابع مشابه
Fast Endomorphism for any Genus 2 Hyperelliptic Curve over a Finite Field of Even Characteristic
In EUROCRYPT 2009, Galbraith, Lin and Scott constructed an efficiently computable endomorphism for a large family of elliptic curves defined over finite fields of large characteristic. They demonstrated that the endomorphism can be used to accelerate scalar multiplication in the elliptic curve cryptosystem based on these curves. In this paper we extend the method to any genus 2 hyperelliptic cu...
متن کاملCo-Z Divisor Addition Formulae in Jacobian of Genus 2 Hyperelliptic Curves over Prime Fields
in this paper we proposed a new approach to divisor scalar multiplication in Jacobian of genus 2 hyperelliptic curves over fields with odd characteristic, without field inversion. It is based on improved addition formulae of the weight 2 divisors in projective divisor representation in most frequent case that suit very well to scalar multiplication algorithms based on Euclidean addition chains....
متن کاملSkew-Frobenius Maps on Hyperelliptic Curves
The hyperelliptic curve cryptosystems take most of the time for computing a scalar multiplication kD of an element D in the Jacobian JC of a hyperelliptic curve C for an integer k. Therefore its efficiency depends on the scalar multiplications. Among the fast scalar multiplication methods, there is a method using a Frobenius map. It uses a Jacobian defined over an extension field of the definit...
متن کاملSpeeding up the Arithmetic on Koblitz Curves of Genus Two
Koblitz, Solinas, and others investigated a family of elliptic curves which admit especially fast elliptic scalar multiplication. They considered elliptic curves deened over the nite eld F 2 with base eld F 2 n. In this paper, we generalize their ideas to hyperelliptic curves of genus 2. Given the two hyperelliptic curves C a : v 2 +uv = u 5 + a u 2 + 1 with a = 0; 1, we show how to speed up th...
متن کاملEfficient Doubling on Genus 3 Curves over Binary Fields
The most important and expensive operation in a hyperelliptic curve cryptosystem (HECC) is scalar multiplication by an integer k, i.e., computing an integer k times a divisor D on the Jacobian. Using some recoding algorithms for scalar k, we can reduce a number of divisor class additions during the process of computing scalar multiplication. So divisor doubling will account for the main part in...
متن کامل