We study the complexity of computing Boolean functions using AND, OR and NOT gates. We show that a circuit of depth d with S gates can be made to output a constant by setting O(S1...
Abstract. In this paper, we generalize the previous formal de nitions of random-self-reducibility. We show that, even under our very general de nition, sets that are complete for a...
We study genus g hyperelliptic curves with reduced automorphism group A5 and give equations y2 = f(x) for such curves in both cases where f(x) is a decomposable polynomial in x2 or...
Let S Rk+m be a compact semi-algebraic set defined by P1 0, . . . , P 0, where Pi R[X1, . . . , Xk, Y1, . . . , Ym], and deg(Pi) 2, 1 i . Let denote the standard projection f...
We show how to construct a variety of “trapdoor” cryptographic tools assuming the worst-case hardness of standard lattice problems (such as approximating the length of the sho...