Designs, Codes and Cryptography
A course in computational algebraic number theory
A course in computational algebraic number theory
On orders of optimal normal basis generators
Mathematics of Computation
Gauss periods: orders and cryptographical applications
Mathematics of Computation
Gauss Periods and Fast Exponentiation in Finite Fields (Extended Abstract)
LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
Massively Parallel Computation of Discrete Logarithms
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Efficient finite field digital-serial multiplier architecture for cryptography applications
Proceedings of the conference on Design, automation and test in Europe
Finite Field Multiplier Using Redundant Representation
IEEE Transactions on Computers
IEEE Transactions on Computers
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Fast Elliptic Curve Point Counting Using Gaussian Normal Basis
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Multiplicative Masking and Power Analysis of AES
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Hardware architectures for public key cryptography
Integration, the VLSI Journal
A Redundant Representation of GF(q^n) for Designing Arithmetic Circuits
IEEE Transactions on Computers
Constructing Composite Field Representations for Efficient Conversion
IEEE Transactions on Computers
IEEE Transactions on Computers
Extractors for binary elliptic curves
Designs, Codes and Cryptography
A high-speed word level finite field multiplier in F2m using redundant representation
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
An Efficient Finite Field Multiplier Using Redundant Representation
ACM Transactions on Embedded Computing Systems (TECS)
Finite field arithmetic using quasi-normal bases
Finite Fields and Their Applications
Rings of Low Multiplicative Complexity
Finite Fields and Their Applications
Quantum binary field inversion: improved circuit depth via choice of basis representation
Quantum Information & Computation
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A method is described for performing computations in a finite field GF(2N) by embedding it in a larger ring Rp where the multiplication operation is a convolution product and the squaring operation is a rearrangement of bits. Multiplication in Rp has complexity N +1, which is approximately twice as efficient as optimal normal basis multiplication (ONB) or Montgomery multiplication in GF(2N), while squaring has approximately the same efficiency as ONB. Inversion and solution of quadratic equations can also be performed at least as fast as previous methods.