Co-Z Divisor Addition Formulae in Jacobian of Genus 2 Hyperelliptic Curves over Prime Fields

نویسندگان

  • Vladyslav Kovtun
  • Irina Sagir
چکیده

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. Keywords-hyperelliptic curve, divisor, Jacobian, addition formulae, exponentiation, projective representation

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Flexible, Prime-Field, Genus 2 Hyperelliptic- Curve Cryptography Processor with Low Power Consumption and Uniform Power Draw

prime-field hyperelliptic-curve cryptography (HECC) processor with uniform power draw. The HECC processor performs divisor scalar multiplication on the Jacobian of genus 2 hyperelliptic curves defined over prime fields for arbitrary field and curve parameters. It supports the most frequent case of divisor doubling and addition. The optimized implementation, which is synthesized in a 0.13 mm sta...

متن کامل

Suitable Curves for Genus-4 HCC over Prime Fields: Point Counting Formulae for Hyperelliptic Curves of Type y2=x2k+1+ax

Computing the order of the Jacobian group of a hyperelliptic curve over a finite field is very important to construct a hyperelliptic curve cryptosystem (HCC), because to construct secure HCC, we need Jacobian groups of order in the form l · c where l is a prime greater than about 2 and c is a very small integer. But even in the case of genus two, known algorithms to compute the order of a Jaco...

متن کامل

Fast Arithmetic In Jacobian Of Hyperelliptic Curves Of Genus 2 Over GF(p)

In this paper, we suggest a new fast transformation for a divisor addition for hyperelliptic curves. The transformation targets the Jacobian of genus-2 curves over odd characteristic fields in projective representation. Compared to previously published results, the modification reduces the computational complexity and makes hyperelliptic curves more attractive for applications.

متن کامل

Efficient 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

Correspondences on Hyperelliptic Curves and Applications to the Discrete Logarithm

The discrete logarithm is an important crypto primitive for public key cryptography. The main source for suitable groups are divisor class groups of carefully chosen curves over finite fields. Because of index-calculus algorithms one has to avoid curves of genus ≥ 4 and non-hyperelliptic curves of genus 3. An important observation of Smith [S] is that for “many” hyperelliptic curves of genus 3 ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • IACR Cryptology ePrint Archive

دوره 2010  شماره 

صفحات  -

تاریخ انتشار 2010