Factoring multivariate polynomials over large finite fields

Da Qing Wan
1990 Mathematics of Computation  
A simple probabilistic algorithm is presented to find the irreducible factors of a bivariate polynomial over a large finite field. For a polynomial f(x, y) over F of total degree n , our algorithm takes at most 4.89, 2 , n log n log q operations in F to factor f(x , y) completely. This improves a probabilistic factorization algorithm of von zur Gathen and Kaltofen, which takes 0(n log n log q) operations to factor f(x, y) completely over F . The algorithm can be easily generalized to factor
more » ... ivariate polynomials over finite fields. We shall give two further applications of the idea involved in the algorithm. One is concerned with exponential sums; the other is related to permutational polynomials over finite fields (a conjecture of Chowla and Zassenhaus).
doi:10.1090/s0025-5718-1990-1011448-0 fatcat:ugxvlbiayrax3oe3ficz3yjkmy