O(log(n)) parallel time finite field inversion
Let p be prime and assume that GF(p n ) is given via an irreducible nth degree GF(p) polynomial. We exhibit a boolean circuit of size n O(1) and depth O(log(n)) such that for any x ε GF(p n ) the circuit produces x −1. The circuit is based upon an interesting connection between finite field computations and the eigenvalues of certain matrices. The issue of circuit uniformity is also considered.
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