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Low-complexity multiplexer-based normal basis multiplier over GF（2^m）

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第6期10卷 834-842页

作者： Jenn-Shyong HORNG I-Chang JOU Chiou-Yng LEE Institute of Engineering Science and Technology National Kaohsiung First University of Science and Technology Department of Computer Information and Network Engineering Lunghwa University of Science and Technology

We present a new normal basis multiplication scheme using a multiplexer-based algorithm. In this algorithm, the proposed multiplier processes in parallel and has a multiplexer-based structure that uses MUX and XOR gates instead of AND and XOR gates. We show that our multiplier for type-1 and type-2 normal bases saves about 8% and 16%, respectively, in space complexity as compared to existing normal basis multipliers. Finally, the proposed architecture has regular and modular con-figurations and is well suited to VLSI implementations.

关键词： Finite field multiplication normal basis Gaussian normal basis Elliptic curve cryptosystem

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Two normal basis Multiplication Algorithms for GF（2^n）

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Tsinghua Science and Technology 2006年第3期11卷 264-270页

作者：樊海宁刘铎戴一奇 Department of Computer Science and Technology Tsinghua University Beijing 100084 China

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（2^n）. The first algorithm is suitable for high complexity normal bases, while the second algorithm is fast for type-I optimal normal bases and low complexity normal bases. Theoretical analyses and experimental results both indicate that the presented algorithms are efficient in GF（2^233）, GF（2^283）, GF（2^409）, and GF（2^571）, 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.

关键词： finite field normal basis multiplication algorithm

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A New Criterion on k-normal Elements over Finite Fields

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Chinese Annals of Mathematics,Series B 2020年第5期41卷 665-678页

作者： Aixian ZHANG Keqin FENG Department of Mathematical Sciences Xi’an University of TechnologyXi’an 710054China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al.(2013).Several methods to construct k-normal elements were presented by Alizadah et al.(2016)and Huczynska et al.(2013),and the criteria on k-normal elements were given by Alizadah et al.(2016)and Antonio et al.(2018).In the paper by Huczynska,S.,Mullen,G.,Panario,*** Thomson,D.(2013),the number of k-normal elements for a fixed finite field extension was calculated and *** this paper the authors present a new criterion on k-normal elements by using idempotents and show some *** criterion was given for usual normal elements before by Zhang et al.(2015).

关键词： normal basis Finite field Idempotent Linearized polynomial Gauss

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On Existence of Primitive normal Elements of Cubic Form over Finite Fields

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Algebra Colloquium 2022年第1期29卷 151-166页

作者： Himangshu Hazarika Dhiren Kumar Basnet Department of Mathematical Sciences Tezpur UniversityAssamIndia

For a prime p and a positive integer k,let q=p^(k) and F_(q)^(n) be the extension field of F_(q).We derive a sufficient condition for the existence of a primitive element α in F_(q)^(n) such that α^(3)-α+1 is also a primitive element of F_(q)^(n) ,a sufficient condition for the existence of a primitive normal element a in F_(q)^(n) over F_(q) such that α(3)-α+1 is a primitive element of F_(q)^(n) ,and a suficient condition for the existence of a primitive normal element a in F_(q)^(n) over F_(q) such that а^(3)-а+1 is also a primitive normal element of F_(q)^(n) over F_(q).

关键词： finite field primitive element free element normal basis character

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