VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
A VLSI Architecture for Fast Inversion in GF(2/sup m/)
IEEE Transactions on Computers
Hardware architectures for public key cryptography
Integration, the VLSI Journal
High-Speed, Low-Complexity Systolic Designs of Novel Iterative Division Algorithms in GF(2^m)
IEEE Transactions on Computers
An extension of TYT algorithm for GF ((2n/)m/) using precomputation
Information Processing Letters
IEEE Transactions on Computers
Parallel Itoh---Tsujii multiplicative inversion algorithm for a special class of trinomials
Designs, Codes and Cryptography
Information Sciences: an International Journal
Implementation and analysis of stream ciphers based on the elliptic curves
Computers and Electrical Engineering
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
IEEE Transactions on Circuits and Systems II: Express Briefs
Low-complexity bit-parallel dual basis multipliers using the modified Booth's algorithm
Computers and Electrical Engineering
Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
An extension of TYT algorithm for GF((2n)m) using precomputation
Information Processing Letters
An extension of TYT inversion algorithm in polynomial basis
Information Processing Letters
A simple stream cipher with proven properties
Cryptography and Communications
Quantum binary field inversion: improved circuit depth via choice of basis representation
Quantum Information & Computation
Hierarchical decoding of double error correcting codes for high speed reliable memories
Proceedings of the 50th Annual Design Automation Conference
Efficient quantum circuits for binary elliptic curve arithmetic: reducing T-gate complexity
Quantum Information & Computation
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A fast algorithm for multiplicative inversion in $GF(2^m)$ using normal basis is proposed. It is an improvement on those proposed by Itoh and Tsujii and by Chang et al., which are based on Fermat's Theorem and require $O(\log m)$ multiplications. The number of multiplications is reduced by decomposing $m-1$ into several factors and a small remainder.