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
IEEE Transactions on Computers - Special issue on computer arithmetic
Matrix computations (3rd ed.)
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
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
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
Generic implementations of elliptic curve cryptography using partial reduction
Proceedings of the 9th ACM conference on Computer and communications security
Mastrovito Multiplier for General Irreducible Polynomials
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Towards Efficient Verification of Arithmetic Algorithms over Galois Fields GF(2m)
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Error Detection in Polynomial Basis Multipliers over Binary Extension Fields
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
An End-to-End Systems Approach to Elliptic Curve Cryptography
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Low Complexity Multiplication in a Finite Field Using Ring Representation
IEEE Transactions on Computers
Hardware architectures for public key cryptography
Integration, the VLSI Journal
Towards fault-tolerant cryptographic computations over finite fields
ACM Transactions on Embedded Computing Systems (TECS)
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
Journal of VLSI Signal Processing Systems
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
Efficient Bit-Parallel Multiplier for Irreducible Pentanomials Using a Shifted Polynomial Basis
IEEE Transactions on Computers
A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields
IEEE Transactions on Computers
An efficient technique for synthesis and optimization of polynomials in GF(2m)
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
A Novel Architecture for Galois Fields GF(2^m) Multipliers Based on Mastrovito Scheme
IEEE Transactions on Computers
Montgomery Residue Representation Fault-Tolerant Computation in GF(2k)
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
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
A cryptographic processor for arbitrary elliptic curves over GF(2m)
A cryptographic processor for arbitrary elliptic curves over GF(2m)
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
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
| Hi-index | 15.01 |
We present a new formulation of the Mastrovito multiplication matrix for the field $GF(2^m)$ generated by an arbitrary irreducible polynomial. We study in detail several specific types of irreducible polynomials, e.g., trinomials, all-one-polynomials, and equally-spaced-polynomials, and obtain the time and space complexity of these designs. Particular examples illustrating the properties of the proposed architecture are also given. The complexity results established in this paper match the best complexity results known to date. The most important new result is the space complexity of the Mastrovito multiplier for an equally-spaced-polynomial, which is found as $(m^2 - \Delta)$ XOR gates and $m^2$ AND gates, where $\Delta$ is the spacing factor.