Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Discrete Applied Mathematics
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 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
IEEE Transactions on Computers
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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(2m). 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 datapath 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-up and an added flexibility toward hardwaresoftware co-design of processors for very large finite fields.