Improved three-way split formulas for binary polynomial multiplication

Download

index.pdf

Date

2011-08-12

Author

Cenk, Murat
Hasan, M. Anwar

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

242
views

0
downloads

In this paper we deal with 3-way split formulas for binary field multiplication with five recursive multiplications of smaller sizes. We first recall the formula proposed by Bernstein at CRYPTO 2009 and derive the complexity of a parallel multiplier based on this formula. We then propose a new set of 3-way split formulas with five recursive multiplications based on field extension. We evaluate their complexities and provide a comparison.

Subject Keywords

Critical Path, Polynomial Multiplication, Elliptic Curve Cryptography, Inductive Relation, Arithmetic Complexity

URI

https://hdl.handle.net/11511/30418

DOI

https://doi.org/10.1007/978-3-642-28496-0_23

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Improved Three-Way Split Formulas for Binary Polynomial and Toeplitz Matrix Vector Products Cenk, Murat; Hasan, M. Anwar (2013-07-01) In this paper, we consider three-way split formulas for binary polynomial multiplication and Toeplitz matrix vector product (TMVP). We first recall the best known three-way split formulas for polynomial multiplication: the formulas with six recursive multiplications given by Sunar in a 2006 IEEE Transactions on Computers paper and the formula with five recursive multiplications proposed by Bernstein at CRYPTO 2009. Second, we propose a new set of three-way split formulas for polynomial multiplication that a...
Some new results on binary polynomial multiplication Cenk, Murat (2015-11-01) This paper presents several methods for reducing the number of bit operations for multiplication of polynomials over the binary field. First, a modified Bernstein's 3-way algorithm is introduced, followed by a new 5-way algorithm. Next, a new 3-way algorithm that improves asymptotic arithmetic complexity compared to Bernstein's 3-way algorithm is introduced. This new algorithm uses three multiplications of one-third size polynomials over the binary field and one multiplication of one-third size polynomials ...
A New Algorithm for Residue Multiplication Modulo 2(521)-1 Ali, Shoukat; Cenk, Murat (2016-12-02) We present a new algorithm for residue multiplication modulo the Mersenne prime p = 2(521) - 1 based on the Toeplitz matrix-vector product. For this modulus, our algorithm yields better result in terms of the total number of operations than the previously known best algorithm of Granger and Scott presented in Public Key Cryptography (PKC) 2015. We have implemented three versions of our algorithm to provide an extensive comparison - according to the best of our knowledge with respect to the well-known algori...
New Efficient Algorithms for Multiplication Over Fields of Characteristic Three Cenk, Murat; Hasan, M. Anwar (2018-03-01) In this paper, we first present an enhancement of the well-known Karatsuba 2-way and 3-way algorithms for characteristic three fields, denoted by where nae1. We then derive a 3-way polynomial multiplication algorithm with five 1/3 sized multiplications that use interpolation in . Following the computation of the arithmetic and delay complexity of the proposed algorithm, we provide the results of our hardware implementation of polynomial multiplications over and . The final proposal is a new 3-way polynomial...
Faster Residue Multiplication Modulo 521-bit Mersenne Prime and an Application to ECC Ali, Shoukat; Cenk, Murat (2018-08-01) We present faster algorithms for the residue multiplication modulo 521-bit Mersenne prime on 32- and 64-bit platforms by using Toeplitz matrix-vector product. The total arithmetic cost of our proposed algorithms is less than that of existing algorithms, with algorithms for 64- and 32-bit residue multiplication giving the best timing results on our test machine. The transition from 64- to 32-bit implementation is full of challenges because the number of limbs doubles and the limbs' bitlengths are cut in half...

Citation Formats

M. Cenk and M. A. Hasan, “Improved three-way split formulas for binary polynomial multiplication,” 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30418.