A Novel Pre-Computation Scheme of Window τNAF for Koblitz Curves
نویسندگان
چکیده
Let Ea : y 2 + xy = x + ax + 1/F2m be a Koblitz curve. The window τ -adic nonadjacent-form (window τNAF) is currently the standard representation system to perform scalar multiplications on Ea by utilizing the Frobenius map τ . Pre-computation is an important part for the window τNAF. In this paper, we first introduce μτ̄ -operations in lambda coordinates (μ = (−1)1−a and τ̄ is the complex conjugate of the complex representation of τ). Efficient formulas of μτ̄ -operations are then derived and used in a novel pre-computation scheme to improve the efficiency of scalar multiplications using window τNAF. Our pre-computation scheme costs 7M+5S, 26M+16S, and 66M+36S for window τNAF with width 4, 5, and 6 respectively whereas the precomputation with the state-of-the-art technique costs 11M+8S, 43M+18S, and 107M+36S. Experimental results show that our pre-computation is about 60% faster, compared to the best pre-computation in the literature. It also shows that we can save from 2.5% to 4.9% on the scalar multiplications using window τNAF with our pre-computation.
منابع مشابه
On the Optimal Pre-Computation of Window τNAF for Koblitz Curves
Koblitz curves have been a nice subject of consideration for both theoretical and practical interests. The window τ -adic algorithm of Solinas (window τNAF) is the most powerful method for computing point multiplication for Koblitz curves. Precomputation plays an important role in improving the performance of point multiplication. In this paper, the concept of optimal pre-computation for window...
متن کاملEfficient Circuitry for Computing τ-adic Non-Adjacent Form
Elliptic curve point multiplication kP on an elliptic curve is required in every elliptic curve cryptosystem. The operation can be significantly accelerated by using a special type of elliptic curves called the Koblitz curves and by representing the integer k in τ -adic nonadjacent form (τNAF). Hardware-friendly modifications of existing τNAF conversion algorithms are presented and an efficient...
متن کاملFast point multiplication on Koblitz curves: Parallelization method and implementations
Point multiplication is required in every elliptic curve cryptosystem and its efficient implementation is essential. Koblitz curves are a family of curves defined over F2m allowing notably faster computation. We discuss implementation of point multiplication on Koblitz curves with parallel field multipliers. We present a novel parallelization method utilizing point operation interleaving. FPGA ...
متن کاملFaster Implementation of Scalar Multiplication on Koblitz Curves
We design a state-of-the-art software implementation of field and elliptic curve arithmetic in standard Koblitz curves at the 128-bit security level. Field arithmetic is carefully crafted by using the best formulae and implementation strategies available, and the increasingly common native support to binary field arithmetic in modern desktop computing platforms. The i-th power of the Frobenius ...
متن کاملHyperelliptic Curve Cryptography
The use of elliptic-curve groups in cryptography, suggested by Miller [1] and Koblitz [2] three decades ago,provides the same level of security for the Discrete Logarithm Problem as multiplicative groups, with much smallerkey sizes and parameters. The idea was refined two years later by Koblitz, who worked with the group formed bythe points of the Jacobian of hyperelliptic curve...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2017 شماره
صفحات -
تاریخ انتشار 2017