This papers introduces several binary scalar multiplication algorithms with applications to cryptography. Remarkably, the proposed algorithms regularly repeat the same pattern when...
We give two short proofs that for fixed d, a d-regular Cayley graph on an Abelian group of order n has second eigenvalue bounded below by d - O(dn-4/d), where the implied constant...
Let be the fundamental group of a finite connected graph G. Let M be an abelian group. A distribution on the boundary of the universal covering tree is an M-valued measure defin...
We study the symmetries of periodic solutions from Hopf bifurcation in systems with finite abelian symmetries. Our main result, the Abelian Hopf H mod K Theorem, gives necessary a...
In this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller's alg...