We describe new algorithms for performing scalar multiplication on supersingular elliptic curves in characteristic three. These curves can be used in pairing-based cryptography. Since in pairing-based protocols besides pairing computations also scalar multiplications are required, and the performance of the latter is not negligible, improving it is clearly important as well. The techniques pres...

A comparison of the growth curves of adapted and unadapted lines of the same strain of Type A or Type B influenza virus in mice has demonstrated that the unadapted lines of virus exhibit a lag phase of growth lasting approximately 12 hours during which little or no multiplication of virus can be demonstrated. Multiplication by the adapted line begins earlier and may be evident as soon as 6 hour...

Multiplication of two n-bit integers produces a 2n-bit product. To allow the result to be stored in the same format as the inputs, many processors return the n least signiicant bits of the product and an overrow ag. This paper describes methods for integer multiplication with overrow detection for unsigned and two's complement numbers. A method for combining unsigned and two's complement intege...

This paper describes the Parallel Universal Matrix Multiplication Algorithms (PUMMA) on distributed memory concurrent computers. The PIJhlMA package includes not only the non-transposed matrix multiplication routine C = A . B. but also transposed multiplication routines C = AT . B, C = A . BT, and C = AT . BT, for a block scattered data distribution. The routines perform efficiently for a wide ...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

The infectivity of a DNA copy of RNA3 from strain S of alfalfa mosaic virus inserted in a pT7-1 plasmid vector (clone 3pT7-1) was tested as circular DNA by coinoculation with RNAs 1, 2 and 4 from strain B (mix Io) on young tobacco leaves. Virus multiplication was monitored by serological detection of the coat protein. Progeny RNA3 derived from circular plasmid DNA 3pT7-1 was of the same length ...

In this work the number of occurrences of a fixed non-zero digit in the width-[Formula: see text] non-adjacent forms of all elements of a lattice in some region (e.g. a ball) is analysed. As bases, expanding endomorphisms with eigenvalues of the same absolute value are allowed. Applications of the main result are on numeral systems with an algebraic integer as base. Those come from efficient sc...

the objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a fibonacci hypercube structure. most of the popular algorithms for parallel matrix multiplication can not run on fibonacci hypercube structure, therefore giving a method that can be run on all structures especially fibonacci hypercube structure is necessary for parallel matr...

We introduce FourQ, a high-security, high-performance elliptic curve that targets the 128­ bit security level. At the highest level, cryptographic scalar multiplications on FourQ can use a fourdimensional Gallant-Lambert-Vanstone decomposition to minimize the total number of elliptic curve group operations. At the group arithmetic level, FourQ admits the use of extended twisted Edwards coordina...