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Chapter and Conference Paper
Construction of Group Rules for VLSI Application
An application of cellular automata (CA) has been proposed for building parallel processing systems, cryptographic hashing functions, and VLSI technology. Recently, Das et al. have reported characterization of...
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Article
Sparse polynomials, redundant bases, gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields
Gauss periods give an exponentiation algorithm that is fast for many finite fields but slow for many other fields. The current paper presents a different method for construction of elements that yield a fast e...
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Chapter and Conference Paper
Unidirectional Two Dimensional Systolic Array for Multiplication in GF(2 m ) Using LSB First Algorithm
The two dimensional systolic array for multiplication in binary field GF(2 m ) with LSB (Least Significant Bit) first algorithm proposed by Yeh et al. has the unfavorable propert...
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Chapter and Conference Paper
A Novel Arithmetic Unit over GF(2 m ) for Low Cost Cryptographic Applications
We present a novel VLSI architecture for division and multiplication in GF(2 m ), aimed at applications in low cost elliptic curve cryptographic processors. A compact and fast ar...
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Chapter and Conference Paper
A New Digit-Serial Systolic Mulitplier for High Performance GF(2 m ) Applications
This paper presents a new digit-serial systolic multiplier over GF(2 m ) for cryptographic applications. The proposed array is based on the most significant digit first (MSD-firs...
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Chapter and Conference Paper
Compact Linear Systolic Arrays for Multiplication Using a Trinomial Basis in GF(2 m ) for High Speed Cryptographic Processors
Many of the cryptographic schemes over small characteristic finite fields are efficiently implemented by using a trinomial basis. In this paper, we present new linear systolic arrays for multiplication in GF(2 ...
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Chapter and Conference Paper
Fast Irreducibility Testing for XTR Using a Gaussian Normal Basis of Low Complexity
XTR appeared in 2000 is a very promising alternative to elliptic curve cryptosystem. Though the basic idea behind XTR is very elegant and universal, one needs to restrict the primes p such as p ≡ 2 mod3 for optim...
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Chapter and Conference Paper
A New Systolic Array for Least Significant Digit First Multiplication in GF(2 m )
This paper presents a new digit-serial systolic multiplier over GF(2 m ) for cryptographic applications. When input data come in continuously, the proposed array produces multipl...
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Chapter and Conference Paper
A Linear Systolic Array for Multiplication in GF(2 m ) for High Speed Cryptographic Processors
We present new designs of low complexity and low latency systolic arrays for multiplication in GF(2 m ) when there is an irreducible all one polynomial (AOP) of degree m. Our pro...
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Chapter and Conference Paper
Efficient Linear Array for Multiplication in GF(2 m ) Using a Normal Basis for Elliptic Curve Cryptography
We present a new sequential normal basis multiplier over GF(2 m ). The gate complexity of our multiplier is significantly reduced from that of Agnew et al. and is comparable to t...
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Chapter and Conference Paper
A New Arithmetic Unit in GF(2m) for Reconfigurable Hardware Implementation
This paper proposes a new arithmetic unit (AU) in GF(2m) for reconfigurable hardware implementation such as FPGAs, which overcomes the well-known drawback of reduced flexibility that is associated with traditiona...
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Chapter and Conference Paper
Gauss Period, Sparse Polynomial, Redundant Basis, and Efficient Exponentiation for a Class of Finite Fields with Small Characteristic
We present an efficient exponentiation algorithm in a finite field GF(q n ) using a Gauss period of type (n,1). Though the Gauss period α of type (n,1) i...
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Chapter and Conference Paper
A Compact and Fast Division Architecture for a Finite Field GF(2m)
Division over a finite field GF(2m) is the most time and area consuming operation. In this paper, A new division architecture for GF(2m) using the standard basis representation is proposed. Based on a modified ve...
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Chapter and Conference Paper
Efficient Exponentiation for a Class of Finite Fields GF(2 n ) Determined by Gauss Periods
We present a fast and compact hardware architecture of exponentiation in a finite field GF(2 n ) determined by a Gauss period of type (n,k) with k ≥ 2. Our construction is based ...