The efficient squaring algorithm plays an important role in large number arithmetic. All multiplication algorithms can be used for squaring large integers, but their performance can be greatly improved by using the standard squaring algorithm. Complement recoding method can be divided into two groups: 1’s complement recoding method and 2’s complement recoding method. In this paper, we propose a...

Squaring and exponentiation of a number are fundamental arithmetic and widely used in the real-time applications such as image processing, digital filtering and cryptography. In this paper, we propose a squaring algorithm of an integer with canonical signed-digit (CSD) number representation. For an n-digit CSD number, our method generates n/4 CSD numbers of 2n-digit length as partial products. ...

In this paper, a high speed squaring circuit for binary numbers is proposed. High speed Vedic multiplier is used for design of the proposed squaring circuit. The key to our success is that only one Vedic multiplier is used instead of four multipliers reported in the literature. In addition, one squaring circuit is used twice. Our proposed Squaring Circuit seems to have better performance in ter...

Modular exponentiation is an important operation in several public-key cryptography. The standard squaring algorithm is well-known and the Guajardo-Paar algorithm fixes the improper carry handling bug produced by the standard squaring algorithm, but produces error-indexing bug. In this paper, one squaring algorithm is proposed, which stores base products into the Look-Up Table before the squari...

Abstract. Multi-precision squaring is a crucial operation for implementation of Elliptic Curve Cryptography. Particularly, when it comes to embedded processors, the operation should be designed carefully to execute expensive ECC operation on resource constrained devices. In order to bridge the gap between high overheads and limited computation capabilities, we present optimized Karatsuba squari...

A new class of moduli called the low-weight polynomial form integers (LWPFIs) is introduced. LWPFIs are expressed in a low-weight, monic polynomial form, p = f(t). While the generalized Mersenne numbers (GMNs) proposed by Solinas allow only powers of two for t, LWPFIs allow any positive integers. In our first proposal of LWPFIs, we limit the coefficients of f(t) to be 0 and ±1, but later we ext...

We introduce a “derandomized” analogue of graph squaring. This operation increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree. One application of this product is an alternative proof of Reingold’s recent breakthrough result that S-T...

Nano-fertilizers are designed in order to gradually release their food contents. They are also manufactured in such a way that the time of their liberation matches with the food product requirement. The use of nano-fertilizers leads to an increase in the efficiency of the consumption of food elements. With regard to the strategic importance of cotton plant and the effects of zinc in increasing ...

Advanced modern processors support Single Instruction Multiple Data (SIMD) instructions (e.g. Intel-AVX, ARM-NEON) and a massive body of research on vector-parallel implementations of modular arithmetic, which are crucial components for modern public-key cryptography ranging from RSA, ElGamal, DSA and ECC, have been conducted. In this paper, we introduce a novel Double Operand Scanning (DOS) me...