Finite field for scientists and engineers
Finite field for scientists and engineers
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
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
New Low-Complexity Bit-Parallel Finite Field Multipliers Using Weakly Dual Bases
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
New algorithms and architectures for arithmetic in gf(2(m)) suitable for elliptic curve cryptography
New algorithms and architectures for arithmetic in gf(2(m)) suitable for elliptic curve cryptography
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Fault Detection Architectures for Field Multiplication Using Polynomial Bases
IEEE Transactions on Computers
Efficient Bit-Parallel Multiplier for Irreducible Pentanomials Using a Shifted Polynomial Basis
IEEE Transactions on Computers
Efficient parallel multiplier in shifted polynomial basis
Journal of Systems Architecture: the EUROMICRO Journal
A Novel Architecture for Galois Fields GF(2^m) Multipliers Based on Mastrovito Scheme
IEEE Transactions on Computers
Versatile multiplier architectures in GF(2k) fields using the Montgomery multiplication algorithm
Integration, the VLSI Journal
Fast elliptic curve cryptography on FPGA
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
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
Low complexity bit-parallel multipliers based on a class of irreducible pentanomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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
Customizable elliptic curve cryptosystems
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
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Parity of the number of irreducible factors for composite polynomials
Finite Fields and Their Applications
The parity of the number of irreducible factors for some pentanomials
Finite Fields and Their Applications
Integration, the VLSI Journal
Low-power and high-speed design of a versatile bit-serial multiplier in finite fields GF(2m)
Integration, the VLSI Journal
Utilization of Pipeline Technique in AOP Based Multipliers with Parallel Inputs
Journal of Signal Processing Systems
New efficient bit-parallel polynomial basis multiplier for special pentanomials
Integration, the VLSI Journal
Information Processing Letters
| Hi-index | 14.99 |
Abstract--The state-of-the-art Galois field GF(2^m) multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally spaced polynomial (ESP). Unfortunately, there exist only a few irreducible ESPs in the range of interest for most of the applications, e.g., error-correcting codes, computer algebra, and elliptic curve cryptography. Furthermore, it is not always possible to find an irreducible trinomial of degree m in this range. For those cases where neither an irreducible trinomial nor an irreducible ESP exists, the use of irreducible pentanomials has been suggested. Irreducible pentanomials are abundant, and there are several eligible candidates for a given m. In this paper, we promote the use of two special types of irreducible pentanomials. We propose new Mastrovito and dual basis multiplier architectures based on these special irreducible pentanomials and give rigorous analyses of their space and time complexity.