Introduction to finite fields and their applications
Introduction to finite fields and their applications
Matrix computations (3rd ed.)
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
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
Efficient Algorithms for Elliptic Curve Cryptosystems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
Look-Up Table-Based Large Finite Field Multiplication in Memory Constrained Cryptosystems
IEEE Transactions on Computers - Special issue on computer arithmetic
IEEE Transactions on Computers
On the Inherent Space Complexity of Fast Parallel Multipliers for GF(2/supm/)
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
Reconfigurable Implementation of Elliptic Curve Crypto Algorithms
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Mastrovito Multiplier for General Irreducible Polynomials
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Complexity of Polynomial Basis Squaring in F2m
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Montgomery Multiplier and Squarer in GF(2m)
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Hardware architectures for public key cryptography
Integration, the VLSI Journal
Parallel Multipliers Based on Special Irreducible Pentanomials
IEEE Transactions on Computers
A Generalized Method for Constructing Subquadratic Complexity GF(2^k) Multipliers
IEEE Transactions on Computers
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Low-Complexity Bit-Parallel Systolic Montgomery Multipliers for Special Classes of GF(2^m)
IEEE Transactions on Computers
Bit-Parallel Finite Field Multipliers for Irreducible Trinomials
IEEE Transactions on Computers
Relationship between GF(2^m) Montgomery and Shifted Polynomial Basis Multiplication Algorithms
IEEE Transactions on Computers
A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields
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
Low complexity bit parallel multiplier for GF (2m) generated by equally-spaced trinomials
Information Processing Letters
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
Complexity analysis of Reed-Solomon decoding over GF(2m) without using syndromes
EURASIP Journal on Wireless Communications and Networking - Advances in Error Control Coding Techniques
Computers and Electrical Engineering
Low complexity bit-parallel multipliers based on a class of irreducible pentanomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
IEEE Transactions on Signal Processing
An extension of TYT inversion algorithm in polynomial basis
Information Processing Letters
A fast finite field multiplier
ARC'07 Proceedings of the 3rd international conference on Reconfigurable computing: architectures, tools and applications
Toward a solution of the reverse engineering problem using FPGAs
Euro-Par'06 Proceedings of the CoreGRID 2006, UNICORE Summit 2006, Petascale Computational Biology and Bioinformatics conference on Parallel processing
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
On efficient implementation of accumulation in finite field over GF(2m) and its applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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
VLSI architecture for bit parallel systolic multipliers for special class of GF(2m) using dual bases
VDAT'12 Proceedings of the 16th international conference on Progress in VLSI Design and Test
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
New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2n)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low-complexity multiplier for GF(2m) based on all-one polynomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Utilization of Pipeline Technique in AOP Based Multipliers with Parallel Inputs
Journal of Signal Processing Systems
Information Processing Letters
| Hi-index | 15.03 |
An efficient algorithm for the multiplication in $GF(2^m)$ was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial $x^m+x+1$ was given as $m^2-1$ XOR and $m^2$ AND gates. In this paper, we describe an architecture based on a new formulation of the multiplication matrix and show that the Mastrovito multiplier for the generating trinomial $x^m+x^n+1$, where $m \not=2n$, also requires $m^2-1$ XOR and $m^2$ AND gates. However, $m^2-m/2$ XOR gates are sufficient when the generating trinomial is of the form $x^m+x^{m/2}+1$ for an even $m$. We also calculate the time complexity of the proposed Mastrovito multiplier and give design examples for the irreducible trinomials $x^7+x^4+1$ and $x^6+x^3+1$.