Journal ArticleDOI
Efficient digit-serial normal basis multipliers over binary extension fields
TLDR
Two digit-serial architectures for normal basis multipliers over (GF(2m)) have the same gate count and gate delay and an algorithm that can considerably reduce the redundancy is developed.Abstract:
In this article, two digit-serial architectures for normal basis multipliers over (GF(2m)) are presented. These two structures have the same gate count and gate delay. We also consider two special cases of optimal normal bases for the two digit-serial architectures. A straightforward implementation leaves gate redundancy in both of them. An algorithm that can considerably reduce the redundancy is also developed. The proposed architectures are compared with the existing ones in terms of gate and time complexities.read more
Citations
More filters
Book ChapterDOI
Introduction to finite fields and their applications: Preface
Rudolf Lidl,Harald Niederreiter +1 more
Journal ArticleDOI
Efficient algorithms and architectures for field multiplication using Gaussian normal bases
TL;DR: This paper presents two vector-level software algorithms which essentially eliminate bit-wise inner product operations for Gaussian normal bases and shows that the software implementation of the proposed algorithm is faster than previously reported normal basis multiplication algorithms.
Journal ArticleDOI
Low complexity word-level sequential normal basis multipliers
Arash Reyhani-Masoleh,M.A. Hasan +1 more
TL;DR: Two classes of architectures for multipliers over the finite field GF(2/sup m/) are proposed, which are highly area efficient and require fewer number of logic gates even when compared with the most area efficient multipliers available in the open literature.
Journal ArticleDOI
WG: A family of stream ciphers with designed randomness properties
Yassir Nawaz,Guang Gong +1 more
TL;DR: This paper presents a family of stream ciphers which generate a keystream with ideal two-level autocorrelation and guarantees other randomness properties, i.e., balance, long period, ideal tuple distribution, and high and exact linear complexity.
Journal ArticleDOI
Low-Complexity Multiplier Architectures for Single and Hybrid-Double Multiplications in Gaussian Normal Bases
TL;DR: A new digit-level hybrid multiplier which performs two successive multiplications with the same latency as the one for one multiplication is proposed to speed up exponentiation and point multiplication whenever double-multiplication is required and the traditional schemes fail due to the data dependencies.
References
More filters
MonographDOI
Introduction to finite fields and their applications
Rudolf Lidl,Harald Niederreiter +1 more
TL;DR: An introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications, especially information theory, algebraic coding theory and cryptology and a chapter on applications within mathematics, such as finite geometries.
Book ChapterDOI
Introduction to finite fields and their applications: Preface
Rudolf Lidl,Harald Niederreiter +1 more
Journal ArticleDOI
VLSI Architectures for Computing Multiplications and Inverses in GF(2 m )
TL;DR: In this article, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m) with the simple squaring property of the normal basis representation used together with this multiplier.
Book
Applications of Finite Fields
TL;DR: The Discrete Logarithm Problem and Elliptic Curves over Finite Fields, and Other Applications.
Patent
Computational method and apparatus for finite field arithmetic
Jimii Kei Oomura,James L. Massey +1 more
TL;DR: In this article, the GF(2 m ) elements are represented by a vector of m binary digits in such a way that multiplication can be performed by using the same logic function to compute each binary component of the product of two elements, and addition can be formed by logic circuitry that forms the modulo-two sum of the corresponding components of the two vectors representing the elements to be summed.