A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Bit serial multiplication in finite fields
SIAM Journal on Discrete Mathematics
Constructive problems for irreducible polynomials over finite fields
Proceedings of the third Canadian workshop on Information theory and applications
On orders of optimal normal basis generators
Mathematics of Computation
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
On Computing Multiplicative Inverses in GF(2/sup m/)
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Exponentiation in Finite Fields: Theory and Practice
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Fast Message Authentication Using Efficient Polynomial Evaluation
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Efficient computations in finite fields with cryptographic significance
Efficient computations in finite fields with cryptographic significance
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Bit-Parallel Finite Field Multipliers for Irreducible Trinomials
IEEE Transactions on Computers
Fault Detection Architectures for Field Multiplication Using Polynomial Bases
IEEE Transactions on Computers
Relationship between GF(2^m) Montgomery and Shifted Polynomial Basis Multiplication Algorithms
IEEE Transactions on Computers
Fast elliptic curve cryptography on FPGA
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A New Bit-Serial Architecture for Field Multiplication Using Polynomial Bases
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field
Journal of Systems Architecture: the EUROMICRO Journal
Improved throughput bit-serial multiplier for GF(2m) fields
Integration, the VLSI Journal
Low complexity bit-parallel multipliers based on a class of irreducible pentanomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low-complexity bit-parallel dual basis multipliers using the modified Booth's algorithm
Computers and Electrical Engineering
An extension of TYT inversion algorithm in polynomial basis
Information Processing Letters
Efficient finite field processor for GF(2163) and its implementation
International Journal of High Performance Systems Architecture
Efficient bit-parallel multipliers over finite fields GF(2m)
Computers and Electrical Engineering
Speedup of bit-parallel Karatsuba multiplier in GF(2 m) generated by trinomials
Information Processing Letters
A high-performance unified-field reconfigurable cryptographic processor
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
On efficient implementation of accumulation in finite field over GF(2m) and its applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Transactions on computational science XI
Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis
Integration, the VLSI Journal
Fast forth power and its application in inversion computation for a special class of trinomials
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
Integration, the VLSI Journal
New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2n)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
On the arithmetic operations over finite fields of characteristic three with low complexity
Journal of Computational and Applied Mathematics
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Bit-parallel finite field multiplication using polynomial basis can be realized in two steps: polynomial multiplication and reduction modulo the irreducible polynomial. In this article, we present an upper complexity bound for the modular polynomial reduction. When the field is generated with an irreducible trinomial, closed form expressions for the coefficients of the product are derived in term of the coefficients of the multiplicands. Complexity of the multiplier architectures and their critical path length is evaluated and they are comparable to the previous proposals for the same class of fields. Analytical form for bit-parallel squaring operation is also presented. The complexities for bit-parallel squarer are also derived when an irreducible trinomial is used. Consequently, it is argued that to solve multiplicative inverse using polynomial basis can be at least as good as using normal basis.