Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Discrete Applied Mathematics
Designs, Codes and Cryptography
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Implementing elliptic curve cryptography
Implementing elliptic curve cryptography
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
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
Efficient Normal Basis Multipliers in Composite Fields
IEEE Transactions on Computers
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
A Search of Minimal Key Functions for Normal Basis Multipliers
IEEE Transactions on Computers
Efficient Software Implementation for Finite Field Multiplication in Normal Basis
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
Fast Normal Basis Multiplication Using General Purpose Processors
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Efficient Algorithms for Elliptic Curve Cryptosystems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Elliptic Scalar Multiplication Using Point Halving
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms and Architectures for Field Multiplication Using Gaussian Normal Bases
IEEE Transactions on Computers
Software Multiplication Using Gaussian Normal Bases
IEEE Transactions on Computers
Journal of VLSI Signal Processing Systems
WG: A family of stream ciphers with designed randomness properties
Information Sciences: an International Journal
On complexity of normal basis multiplier using modified Booth's algorithm
AIC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Applied Informatics and Communications - Volume 7
On complexity of normal basis multiplier using modified Booth's algorithm
AIC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Applied Informatics and Communications - Volume 7
Low-complexity bit-parallel dual basis multipliers using the modified Booth's algorithm
Computers and Electrical Engineering
On the (im)possibility of practical and secure nonlinear filters and combiners
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Scalable Gaussian Normal Basis Multipliers over GF(2m) Using Hankel Matrix-Vector Representation
Journal of Signal Processing Systems
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For cryptographic applications, normal bases have received considerable attention, especially for hardware implementation. In this article, we consider fast software algorithms for normal basis multiplication over the extended binary field GF (2^m). We present a vector-level algorithm which essentially eliminates the bit-wise inner products needed in the conventional approach to the normal basis multiplication. We then present another algorithm which significantly reduces the dynamic instruction counts. Both algorithms utilize the full width of the data-path of the general purpose processor on which the software is to be executed. We also consider composite fields and present an algorithm which can provide further speed-ups and an added flexibility toward hardware-software codesign of processors for very large finite fields.