Parallel Computation of Division over GF(2^n) Covering Divide-by-Zero Based on Tile Assembly Model

This paper proposes how to compute division over finite field GF(2ⁿ) that could cover the case of zero divisor based on tile assembly model. Key functions are accomplished by combining n final configurations of two different sub-models. The final configuration of every sub-model contains 2n²-n computation tiles which perform 10 different functions. The coding ways of most computation tiles are optimized than the previous model to improve the complexity. The highest bit of modulus number is omitted to simplify the encoding way of computation tiles in the assembly process. This model requires 4591 types of computation tiles and 13 types of boundary tiles. The assembly time complexity is 2n²-1 and the space complexity is n⁴.