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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
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
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
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 ...