Irreducibility testing of lacunary 0, 1-polynomials

A reciprocal polynomial g(x) ∈ Z[x] is such that g(0) 6= 0 and if g(α) = 0 then g(1/α) = 0. The non-reciprocal part of a monic polynomial f(x) ∈ Z[x] is f(x) divided by the product of its irreducible monic reciprocal factors (to their multiplicity). This paper presents an algorithm for testing the irreducibility of the nonreciprocal part of a 0, 1-polynomial (a polynomial having each coefficient either 0 or 1). The algorithm runs in time O(2rr log r log n) where r is the number of non-zero terms of the input polynomial and n is its degree. Thus, the algorithm efficiently handles lacunary (or sparse) 0, 1-polynomials. above keywords.