Improving the time complexity of the computation of irreducible and primitive polynomials in finite fields [chapter]

Josep Rifà, Joan Borrell
1991 Lecture Notes in Computer Science  
In this paper, we present a method to compute all the irreducible and primitive polynomials of degree m over a finite field. We also describe two concrete implementations of our method with respective time complexities O(m 2 + m log rn) and O(m 2 ÷ logm). These implementations, using in parallel different devices introduced to operate in these fields [1], [7], allows us to reduce the time complexity of our method below that of the best previously known methods [3]. Our algorithm is especially
more » ... ll-suited for applications using large finite fields.
doi:10.1007/3-540-54522-0_123 fatcat:2im7ejbtnfa5lpsrp5ddjfxjxy