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
Systolic Array Implementation of Euclid's Algorithm for Inversion and Division in GF (2m)
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
Elliptic curves in cryptography
Elliptic curves in cryptography
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes
Designs, Codes and Cryptography
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
New Systolic Architectures for Inversion and Division in GF(2^m)
IEEE Transactions on Computers
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Parallel Itoh---Tsujii multiplicative inversion algorithm for a special class of trinomials
Designs, Codes and Cryptography
Computers and Electrical Engineering
Low-Complexity Bit-Parallel Square Root Computation over GF(2^{m}) for All Trinomials
IEEE Transactions on Computers
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This contribution is concerned with an improvement of Itoh and Tsujii's algorithm for inversion in finite field GF(2m) using polynomial basis. Unlike the standard version of this algorithm, the proposed algorithm uses forth power and multiplication as main operations. When the field is generated with a special class of irreducible trinomials, an analytical form for fast bit-parallel forth power operation is presented. The proposal can save 1TX compared with the classic approach, where TX is the delay of one 2-input XOR gate. Based on this result, the proposed algorithm for inversion achieves even faster performance, roughly improves the delay by $\frac{m}{2}T_X$, at the cost of slight increase in the space complexity compared with the standard version. To the best of our knowledge, this is the first work that proposes the use of forth power in computation of multiplicative inverse using polynomial basis and shows that it can be efficient.