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

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... 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).