Usage of Optimal Extension Fields for Elliptic Curve Cryptosystems

نویسندگان

  • Tetsutaro Kobayashi
  • Kazumaro Aoki
  • Fumitaka Hoshino
  • Kunio Kobayashi
  • Hikaru Morita
چکیده

In IEEE P1363, two kinds of finite fields, “Prime Finite Fields” and “Characteristic Two Finite Fields” have been standardized. We propose “Optimal Extension Fields (OEF)” in addition to the two fields. OEF is efficient to compute [1–3].

برای دانلود 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

Efficient elliptic curve cryptosystems

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

متن کامل

A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields

This paper shows that many of elliptic curve cryptosystems over quartic extension fields of odd characteristics are reduced to genus two hyperelliptic curve cryptosystems over quadratic extension fields. Moreover, it shows that almost all of the genus two hyperelliptic curve cryptosystems over quadratic extension fields of odd characteristics come under Weil descent attack. This means that many...

متن کامل

Optimal Extension Fields for Fast Arithmetic in Public - Keyalgorithmsa

This report introduces a new class of Galois eld used to achieve fast nite eld arithmetic which we call an Optimal Extension Field (OEF). This approach is well suited for implementation of public-key cryptosystems based on elliptic and hyperelliptic curves on RISC workstations. We de ne OEFs and describe methods for their construction. In addition, we demonstrate that use of an OEF yields the f...

متن کامل

On Implementation of GHS Attack against Elliptic Curve Cryptosystems over Cubic Extension Fields of Odd Characteristics

In this paper, we present algorithms for implementation of the GHS attack to Elliptic curve cryptosystems (ECC). In particular, we consider two large classes of elliptic curves over cubic extension fields of odd characteristics which have weak covering curves against GHS attack, whose existence have been shown recently [16][17][18]. We show an algorithm to find definition equation of the coveri...

متن کامل

Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms

This contribution introduces a class of Galois eld used to achieve fast nite eld arithmetic which we call an Optimal Extension Field OEF This approach is well suited for implementation of public key cryptosystems based on elliptic and hyperelliptic curves Whereas previous reported optimizations focus on nite elds of the form GF p and GF m an OEF is the class of elds GF p for p a prime of specia...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007