Fast Polynomial Factorization Over High Algebraic Extensions of Finite Fields

New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n1+a , where a > 0 is constant, these algorithms are asymptotically faster than previous known algorithms, the fastest of which required time Ω(n(log q)2 ),† or Ω(n3+2a ) in this case, which corresponds to the cost of computing xq modulo an n degree polynomial. The new algorithms factor an arbitrary polynomial in time O(n3+a+o(1)

• Type: Conference
• Year: 1997
• Where: ISSAC
• Authors: Erich Kaltofen, Victor Shoup
• Keywords: ISSAC 1997, Mathematics, Polynomial, Prime Number, finite field