Modular exponentiation is one of the most important operations in public-key cryptosystems. A modular exponentiation is composed of repetition of modular multiplications. Again, the modular multiplication consists of a multi-precision multiplication and a modular reduction. Therefore, we can reduce the execution time of the modular exponentiation by two methods. One is to reduce the number of m...

Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as computing GCD and residue operation require at most a factor of logn time more than multiplication. We propose an integer multiplication algorithm using Nikhila...

The different methods used in the multiplication of numbers are long method (column method) multiplication, grid and addition multiplication. utilization mentioned to solve power (index) base number (number that multiply itself a times) horrendous, outrageous, tedious, time consuming too be carried out. This study develops computation using Kifilideen (matrix, combination distributive (MCD)) ap...

The Strassen algorithm and Winograd’s variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate singleas well as double-precision matrix multiplication by using these algorithms, no research to date has been undertaken to accelerate multiple precision matrix multiplication. In this pa...

This thesis discusses the matrix container template I implemented as part of the STXXL library for very large data sets. Because it is designed for matrices too big to be held in internal memory, algorithms and data structures are chosen to be efficient for external memory operation. Transposition, addition, and scalar multiplication are easy; therefore their description is kept brief. Matrix m...

Truncated multiplications compute truncated products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(nα), with 1 < α ≤ 2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications, several cryptographic long i...

The most popular public-key cryptography systems nowadays are RSA and Elliptic Curve Cryptography (ECC). ECC is a type of public-key cryptosystem which uses the additive group of points on a nonsingular elliptic curve as a cryptographic medium. The basic operation in most elliptic curve cryptosystems is a scalar multiplication. Scalar Multiplication is the costliest operation among all in ECC w...

In this paper, we show efficient implementations of binary field multiplication over ARMv8. We exploit an advanced 64-bit polynomial multiplication (PMULL) supported by ARMv8 and conduct multiple levels of asymptotically faster Karatsuba multiplication. Finally, our method conducts binary field multiplication within 57 clock cycles for B-251. Our proposed method on ARMv8 improves the performanc...

Multiplication of Toxoplasma gondii was examined in vitro in murine erythroid cells at different stages of development. Toxoplasma gondii multiplied in nucleated erythroblasts and enucleated reticulocytes from the foetal liver, and in immature reticulocytes and yolk-sac derived erythrocytes from the foetal circulation. However, the rate of multiplication was lowered as erythroblasts matured, an...

ABSTRACT This paper introduces a novel generalized concept of higher order heart-oriented rhotrix multiplication expression. The multiplication method we adapted is intended to maintain the unique properties associated with the initial definition of rhotrix. The special multiplication process can be used to solve various problems involving n x n rhotrices multiplication. Most importantly a gene...