| Two Normal Basis Multiplication Algorithms for GF（2^n） |
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| 引用本文： | 樊海宁,刘铎,戴一奇.Two Normal Basis Multiplication Algorithms for GF（2^n）[J].清华大学学报,2006,11(3):264-270. |
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| 作者姓名： | 樊海宁 刘铎 戴一奇 |
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| 作者单位： | Department of Computer Science and Technology Tsinghua University Beijing 100084 China，Department of Computer Science and Technology，Tsinghua University Beijing 100084 China，Department of Computer Science and Technology，Tsinghua University Beijing 100084 China |
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| 基金项目： | SupportedbytheNationalNaturalScienceFoundationofChina(No.90304014)andtheNationalHigh-TechResearchandDevel-opment(863)ProgramofChina(No.2005AA114160) |
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| 摘 要： | Introduction Arithmetic operations in GF(2n)play an important role in coding theory,computer algebra,and cryptosystems.Among the different types of field representations,the normal basis(NB)has received considerable attention on account of its efficient i…
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| 关 键 词： | 有限域 正规基 乘法算法 ECDSA |
| 收稿时间： | 2004-09-16 |
| 修稿时间： | 2004-09-162005-03-31 |
Two Normal Basis Multiplication Algorithms for GF(2n) |
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| FAN Haining,LIU Duo,DAI Yiqi.Two Normal Basis Multiplication Algorithms for GF(2n)[J].Tsinghua Science and Technology,2006,11(3):264-270. |
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| Authors: | FAN Haining LIU Duo DAI Yiqi |
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| Institution: | Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China |
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| Abstract: | For software implementations, word-level normal basis multiplication algorithms utilize the full data-path of the processor, and hence are more efficient than the bit-level multiplication algorithm presented in the IEEE standard P1363-2000. In this paper, two word-level normal basis multiplication algorithms are proposed for GF(2n). The first algorithm is suitable for high complexity normal bases, while the second algo-rithm is fast for type-I optimal normal bases and low complexity normal bases. Theoretical analyses and ex-perimental results both indicate that the presented algorithms are efficient in GF(2233), GF(2283), GF(2409), and GF(2571), which are four of the five binary fields recommended by the National Institute of Standards and Technology (NIST) for the elliptic curve digital signature algorithm (ECDSA) applications. |
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| Keywords: | finite field normal basis multiplication algorithm |
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