Introduction to finite fields and their applications
Introduction to finite fields and their applications
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Low Complexity Bit-Parallel Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
IEEE Transactions on Computers
IEEE Transactions on Computers
A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis
IEEE Transactions on Computers
Handbook of Applied Cryptography
Handbook of Applied Cryptography
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
A New Hardware Architecture for Operations in GF(2m)
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Finite Field Multiplier Using Redundant Representation
IEEE Transactions on Computers
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Efficient Multiplication Beyond Optimal Normal Bases
IEEE Transactions on Computers
A Redundant Representation of GF(q^n) for Designing Arithmetic Circuits
IEEE Transactions on Computers
A Novel Architecture for Galois Fields GF(2^m) Multipliers Based on Mastrovito Scheme
IEEE Transactions on Computers
Low complexity bit parallel multiplier for GF (2m) generated by equally-spaced trinomials
Information Processing Letters
Proceedings of the 2009 Asia and South Pacific Design Automation Conference
Speedup of bit-parallel Karatsuba multiplier in GF(2 m) generated by trinomials
Information Processing Letters
Low-complexity multiplier for GF(2m) based on all-one polynomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
New efficient bit-parallel polynomial basis multiplier for special pentanomials
Integration, the VLSI Journal
Information Processing Letters
| Hi-index | 14.99 |
This paper presents a new bit-parallel multiplier for the finite field GF(2^m) defined by an irreducible all-one polynomial. In order to reduce the complexity of the multiplier, we introduce a redundant representation and use the well-known multiplication method proposed by Karatsuba. The main idea is to combine the redundant representation and the Karatsuba method to design an efficient bit-parallel multiplier. As a result, the proposed multiplier requires about 25 percent fewer AND/XOR gates than the previously proposed multipliers using an all-one polynomial, while it has almost the same time delay as the previously proposed ones.