A course in number theory and cryptography
A course in number theory and cryptography
Computational methods in commutative algebra and algebraic geometry
Computational methods in commutative algebra and algebraic geometry
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
IEEE Transactions on Computers
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
IEEE Transactions on Computers
IEEE Transactions on Computers
Coding Theory and Cryptography: The Essentials
Coding Theory and Cryptography: The Essentials
VLSI Algorithms, Architectures, and Implementation of a Versatile GF(2m) Processor
IEEE Transactions on Computers
Synthesis of integer multipliers in sum of pseudoproducts form
Integration, the VLSI Journal
Software Multiplication Using Gaussian Normal Bases
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
Comb Architectures for Finite Field Multiplication in F(2^m)
IEEE Transactions on Computers
Novel algebraic structure for cyclic codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
| Hi-index | 14.99 |
Elements of a finite field, GF(2^m ), are represented as elements in a ring in which multiplication is more time efficient. This leads to faster multipliers with a modest increase in the number of XOR and AND gates needed to construct the multiplier. Such multipliers are used in error control coding and cryptography. We consider rings modulo trinomials and 4-term polynomials. In each case, we show that our multiplier is faster than multipliers over elements in a finite field defined by irreducible pentanomials. These results are especially significant in the field of elliptic curve cryptography, where pentanomials are used to define finite fields. Finally, an efficient systolic implementation of a multiplier for elements in a ring defined by x^n + x + 1 is presented.