Elliptic curve cryptography (ECC) is one of the most promising public-key techniques in terms of short key size and various crypto protocols. For this reason, many studies on the implementation of ECC on resource-constrained devices within a practical execution time have been conducted. To this end, we must focus on scalar multiplication, which is the most expensive operation in ECC. A number o...

We characterize the multiplication table of an algebra with a multiplicative unity and derive properties of multiplication tables and associated quadratic forms, which allow eecient computation. We compare several ways of computing a multiplication table and associated quadratic forms. By index permutation the complexity of the computation time of associated quadratic forms can be reduced. Expl...

Piece-wise first- and second-order approximations are employed to design commonly used elementary function generators for neural-network emulators. Three novel schemes are proposed for the first-order approximations. The first scheme requires one multiplication, one addition, and a 28-byte lookup table. The second scheme requires one addition, a 14-byte lookup table, and no multiplication. The ...

We demonstrate the high-speed computation of core elliptic curve operations with full protection against timing-type side-channel attacks. We use a state-of-the-art GLV-GLS curve in twisted Edwards form defined over a quadratic extension field of large prime characteristic, which supports a four dimensional decomposition of the scalar. We present highly optimized algorithms and formulas for spe...

We investigate the following generalisation of the ‘multiplication table problem’ of Erdős: given a bipartite graph with m edges, how large is the set of sizes of its induced subgraphs? Erdős’s problem, posed in 1955, of estimating the number of distinct products ab with a, b ≤ n is precisely the problem under consideration when the graph in question is the complete bipartite graph Kn,n. In thi...

Let G be a finite group and C(G) be the family of representative conjugacy classes of‎ ‎subgroups of G‎. ‎The matrix whose H,K-entry is the number of ‎fixed points of the set G/K under the action of H is called the‎ ‎table of marks of G where H,K run through all elements in‎ C(G)‎. Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...

Susumu TANABÉ Abstract. This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system (Theorem 2.7). We examine further how the multiplication table on the Jacobian quotient module calculates the logarithmic vector fields tangent to the discriminan...