Fast and Efficient Galois Field Binary Arithmetic Procedures in C/C++

We have developed algorithms and code for linear algebra and other transforms which utilize standard compiler 16-bit and 32-bit integer arithmetic. We need to transition these algorithms to Composite Finite Field Binary Arithmetic and so, in the first instance, we need a competent mathematician/ programmer to provide us with highly efficient C/C++ code procedures for Galois Field GF(q) ( p = 2, q = p^m ) arithmetic for +, -, *, and / (add, subtract, multiply and divide) for 8-bit, 10-bit, 16-bit, 24-bit and 32-bit binary words ie for m = 8, 10, 16, 24 and 32 with p = 2. Judicious use of log/look-up tables to increase calculation speed encouraged. Speed tested standalone procedures required for each of the 5 composite fields. Programmer capability needs to be tested and proven by providing code for m = 16 and 24 say, with execution times compared with a readily available ‘free’ Fast Galois Field Arithmetic Library. Mathematica notebook attached shows typical examples of linear transforms converted to Prime Finite Field GF(257) (p = 257, m = 1) arithmetic. We require to do Composite Finite Field (p=2) conversions of these type of linear transforms.

Skills: Algorithm, C++ Programming, Cryptography, Mathematics, Matlab and Mathematica

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