Fast Bit-Parallel Polynomial Basis Multiplier for GF(2~m) Defined by Pentanomials Using Weakly Dual Basis

Sun-Mi PARK; Ku-Young CHANG; Dowon HONG; Changho SEO

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Fast Bit-Parallel Polynomial Basis Multiplier for GF(2~m) Defined by Pentanomials Using Weakly Dual Basis

机译：由五项式使用弱对偶基定义的GF（2〜m）快速位并行多项式基乘

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摘要

In this paper, we derive a fast polynomial basis multiplier for GF(2~m) denned by pentanomials x~m + x~(k_3) + x~(k_2) + x~(k_1) + 1 with 1 ≤ k_1 < k_2 < k_3 ≤ m/2 using the presented method by Park and Chang. The proposed multiplier has the time delay T_A + (2 + [log_2(m ~ 1)])T_x or T_A + (3 + [log_2(m - 1)])T_x which is the lowest one compared with known multipliers for pentanomials except for special types, where T_A and T_X denote the delays of one AND gate and one XOR gate, respectively. On the other hand, its space complexity is very slightly greater than the best known results.

机译：在本文中，我们得出了由五项式x〜m + x〜（k_3）+ x〜（k_2）+ x〜（k_1）+ 1定义的GF（2〜m）的快速多项式基乘数，其中1≤k_1

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来源
《IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences》 |2013年第1期|322-331|共10页
作者
Sun-Mi PARK; Ku-Young CHANG; Dowon HONG; Changho SEO;
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作者单位

Department of Applied Mathematics, Kongju National University, 182 Singwan-dong, Gongju-si, Chungnam, 314-701, Korea;

Cryptography Research Team, Electronics and Telecommunications Research Institute, Korea;

Department of Applied Mathematics, Kongju National University, 182 Singwan-dong, Gongju-si, Chungnam, 314-701, Korea;

Department of Applied Mathematics, Kongju National University, 182 Singwan-dong, Gongju-si, Chungnam, 314-701, Korea;

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正文语种 eng
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finite field arithmetic; pentanomials; bit-parallel multiplier; polynomial basis; weakly dual basis;

机译：有限域算法五旬期位并行乘法器;多项式基础弱对偶;

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1. Fast Bit-Parallel Shifted Polynomial Basis Multiplier Using Weakly Dual Basis Over [J] . Park S.-M., Chang K.-Y. Very Large Scale Integration (VLSI) Systems, IEEE Transactions on . 2011,第12期

机译：使用弱对偶基乘的快速位-并行移位多项式基乘
2. New efficient bit-parallel polynomial basis multiplier for special pentanomials [J] . Sun-Mi Park, Ku-Young Chang, Dowon Hong, Integration . 2014,第1期

机译：适用于特殊五项式的新有效位并行多项式基乘
3. Low complexity bit-parallel polynomial basis multipliers over binary fields for special irreducible pentanomials [J] . Jose L. Imana, Roman Hermida, Francisco Tirado Integration . 2013,第2期

机译：用于特殊不可约五项式的二进制字段上的低复杂度位并行多项式基乘
4. A systolic bit-parallel multiplier with flexible latency and complexity over GF(2m) using polynomial basis [C] . Jingxian Zhang, Zheng Song, Qingsheng Hu International conference on advanced materials and engineering materials . 2012

机译：使用多项式在GF（2m）上具有灵活的延迟和复杂性的脉动比特并行乘法器
5. Effects of low-crude protein amino-acid supplemented diets formulated on Lysine:Net energy basis and ractopamine on growth performance and IGF-I and IGFBP-3 mRNA expression in late-finishing pigs. [D] . Moreno, Roman. 2009

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6. Inhomogeneous basis set of symmetric polynomials defined by tableaux. [O] . L C Biedenharn, J D Louck 1990

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7. High-speed polynomial basis multipliers over GF(2(m)) for special pentanomial. [O] . Imaña Pascual José Luis 2016

机译：特殊五项式在GF（2（m））上的高速多项式基乘数。
8. An algorithm to design finite field multipliers using a self-dual normal basis [R] . Wang, C. C. 1987

机译：一种利用自对偶正规基础设计有限域乘法器的算法

Fast Bit-Parallel Polynomial Basis Multiplier for GF(2~m) Defined by Pentanomials Using Weakly Dual Basis

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