VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
Bit serial multiplication in finite fields
SIAM Journal on Discrete Mathematics
IEEE Transactions on Computers - Special issue on computer arithmetic
Efficient Multiplier Architectures for Galois Fields GF(24n)
IEEE Transactions on Computers
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
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
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Software Exponentiation in GF(2^k)
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
A Scalable Dual-Field Elliptic Curve Cryptographic Processor
IEEE Transactions on Computers
Hardware architectures for public key cryptography
Integration, the VLSI Journal
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
Relationship between GF(2^m) Montgomery and Shifted Polynomial Basis Multiplication Algorithms
IEEE Transactions on Computers
High-speed hardware implementations of Elliptic Curve Cryptography: A survey
Journal of Systems Architecture: the EUROMICRO Journal
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
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Fast Reconfigurable Elliptic Curve Cryptography Acceleration for GF(2m) on 32 bit Processors
Journal of Signal Processing Systems
Low complexity digit serial systolic montgomery multipliers for special class of GF(2m)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Speedup of bit-parallel Karatsuba multiplier in GF(2 m) generated by trinomials
Information Processing Letters
Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis
Integration, the VLSI Journal
Efficient gröbner basis reductions for formal verification of galois field multipliers
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
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Montgomery multiplication in {\rm GF}(2^m) is defined by a(x)b(x)r^{-1}(x)\bmod{f(x)}, where the field is generated by a root of the irreducible polynomial f(x), a(x) and b(x) are two field elements in {\rm GF}(2^m), and r(x) is a fixed field element in {\rm GF}(2^m). In this paper, first, a slightly generalized Montgomery multiplication algorithm in {\rm GF}(2^m) is presented. Then, by choosing r(x) according to f(x), we show that efficient architectures of bit-parallel Montgomery multiplier and squarer can be obtained for the fields generated with an irreducible trinomial. Complexities of the Montgomery multiplier and squarer in terms of gate counts and time delay of the circuits are investigated and found to be as good as or better than that of previous proposals for the same class of fields.