Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication

نویسندگان

  • Hwajeong Seo
  • Hyunjin Kim
  • Taehwan Park
  • Yeoncheol Lee
  • Zhe Liu
  • Howon Kim
چکیده

Elliptic curve cryptography (ECC) is one of the most promising public-key techniques in terms of short key size and various crypto protocols. For this reason, many studies on the implementation of ECC on resource-constrained devices within a practical execution time have been conducted. To this end, we must focus on scalar multiplication, which is the most expensive operation in ECC. A number of studies have proposed pre-computation and advanced scalar multiplication using a non-adjacent form (NAF) representation, and more sophisticated approaches have employed a width-w NAF representation and a modified pre-computation table. In this paper, we propose a new pre-computation method in which zero occurrences are much more frequent than in previous methods. This method can be applied to ordinary group scalar multiplication, but it requires large pre-computation table, so we combined the previous method with ours for practical purposes. This novel structure establishes a new feature that adjusts speed performance and table size finely, so we can customize the pre-computation table for our own purposes. Finally, we can establish a customized look-up table for embedded microprocessors.

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

Analysis of the Hamming Weight of the Extended wmbNAF

Scalar multiplication is an important operation in elliptic curve cryptosystems(ECC). The algorithms for computing scalar multiplication are mostly based on the binary expansions of scalars, such as the non-adjacent form (NAF) and wNAF(sliding window method). Representing scalars using more bases can speed up the scalar multiplication, such as mbNAF, wmbNAF and extended wmbNAF, which was propos...

متن کامل

Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication

Recently, the new Multibase Non-Adjacent Form (mbNAF) method was introduced and shown to speed up the execution of the scalar multiplication with an efficient use of multiple bases to represent the scalar. In this work, we first optimize the previous method using fractional windows, and then introduce further improvements to achieve additional cost reductions. Moreover, we present new improveme...

متن کامل

Setting Speed Records with the (Fractional) Multibase Non-Adjacent Form Method for Efficient Elliptic Curve Scalar Multiplication

In this paper, we introduce the Fractional Window-w Multibase NonAdjacent Form (Frac-wmbNAF) method to perform the scalar multiplication. This method generalizes the recently developed Window-w mbNAF (wmbNAF) method by allowing an unrestricted number of precomputed points. We then make a comprehensive analysis of the most recent and relevant methods existent in the literature for the ECC scalar...

متن کامل

Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas

This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient 3P formula in λ-projective coordinates and 5P formula in both affine and λ-projective coordinates. Secondly, extensive experiments have been conducted to test various multi-base scalar multiplication methods (e.g., greedy, ternary/binary, multi...

متن کامل

Symmetric digit sets for elliptic curve scalar multiplication without precomputation

We describe a method to perform scalar multiplication on two classes of ordinary elliptic curves, namely [Formula: see text] in prime characteristic [Formula: see text], and [Formula: see text] in prime characteristic [Formula: see text]. On these curves, the 4-th and 6-th roots of unity act as (computationally efficient) endomorphisms. In order to optimise the scalar multiplication, we conside...

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 13  شماره 

صفحات  -

تاریخ انتشار 2013