In this paper, we propose a novel parallel architecture for fast hardware implementation of elliptic curve point multiplication (ECPM), which is the key operation of an elliptic curve cryptography processor. The point multiplication over binary fields is synthesized on both FPGA and ASIC technology by designing fast elliptic curve group operations in Jacobian projective coordinates. A novel com...

An improvement upon the naive O(n3) algorithm for matrix multiplication was first presented by Strassen, obtaining the result in only O(n2.81) field operations [5]. This raises the question of what the best possible exponent k such that matrix multiplication can be carried out in at most O(nk) time is. Clearly k ≥ 2, since n2 is the size of the output. It is believed that the optimal k is exact...

I point out a simple algebraic error in Joy Christian’s refutation of Bell’s theorem. In substituting the result of multiplying some derived bivectors with one another by consultation of their multiplication table, he confuses the generic vectors which he used to define the table, with other specific vectors having a special role in the paper, which had been introduced earlier. The result shoul...

This survey is devoted to a new algebraic structure called qualgebra. Our topologicalmotivation is the study of knotted 3-valent graphs and closely related branched braids via combinatorially defined coloring invariants. From an algebraic viewpoint, our structure a part of an alternative axiomatization of groups, describing the properties of conjugation operation and its interactions with the g...

For a finite loop Q, let P (Q) be the set of elements that can be represented as a product containing each element of Q precisely once. Motivated by the recent proof of the Hall-Paige conjecture, we prove several universal implications between the following conditions: (A) Q has a complete mapping, i.e. the multiplication table of Q has a transversal, (B) there is no N EQ such that |N | is odd ...

For a finite loop Q, let P (Q) be the set of elements that can be represented as a product containing each element of Q precisely once. Motivated by the recent proof of the Hall-Paige conjecture, we prove several universal implications between the following conditions: (A) Q has a complete mapping, i.e. the multiplication table of Q has a transversal, (B) there is no N E Q such that |N | is odd...