Introduction to finite fields and their applications
Introduction to finite fields and their applications
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Low Complexity Bit-Parallel Squarer for GF(2n) Defined by Irreducible Trinomials
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Bit-Serial and Bit-Parallel Montgomery Multiplication and Squaring over GF(2^m)
IEEE Transactions on Computers
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
New efficient bit-parallel polynomial basis multiplier for special pentanomials
Integration, the VLSI Journal
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I present a new method to compute a bit-parallel polynomial basis squarer for GF(2^m) generated by an arbitrary irreducible polynomial using weakly dual basis. I apply the proposed method to irreducible pentanomial and derive the explicit formulae for squarer. It is the first time that gives the explicit formulae and an upper complexity bound of squarer for irreducible pentanomials. Moreover, such formulae permit one to choose pentanomial for any odd m@?[19,2000] whose multiplier, as well as squarer, can be performed more efficiently.