The point of this paper is to create a basis for apply efficient encryption schemes in wireless communications and in devices with low computing power and resources. Elliptic Curve Cryptography (ECC) fits well for an efficient and secure encryption scheme. It is more efficient than the traditional integer based RSA schemes because ECC utilizes smaller key sizes for equivalent security. A compar...

We document our development of a library for elliptic curve cryptography in JavaScript. We discuss design choices and investigate optimizations at various levels, from integer multiplication and field selection to various fixed-based EC point multiplication techniques. Relying on a small volume of public precomputed data, our code provides a speed-up of a factor 50 compared to previous existing...

In this paper we describe Cryptography by using Karatsuba multipliers and ASCII codes implementing through coordinate geometry for data encryption and decryption with its code in matlab. Elliptic curve cryptography is an asymmetric key cryptography. It includes (i) public key generation on the elliptic curve and its declaration for data encryption and (ii) private key generation and its use in ...

Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S = (2P + Q) from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is fas...

We propose several new methods to protect the scalar multiplication on an elliptic curve against Differential Analysis. The basic idea consists in transforming the curve through various random morphisms to provide a non-deterministic execution of the algorithm. The solutions we suggest complement and improve the state-of-the-art, but also provide a practical toolbox of efficient countermeasures...

The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that realize substantial (often dramatic) performan...

This paper presents an area efficient FPGA implementation approach of the elliptic curve cryptography. There are many retreats in current encryption algorithms (RSA; AES) in respect of security, power & resources at real-time performance [6]. The Elliptic Curve cryptography (ECC) is developing as an important cryptography, and shows a promise to be an alternative of RSA. Small size, high securi...

Elliptic Curve Cryptography is one of the most interested research topic in VLSI. Network security is becoming more and more crucial as the volume of data being exchanged on the Internet increases. ECC offers high security for networking and communication. FPGA based architecture for elliptic curve cryptography coprocessor ,which has promising performance in terms of both Space Complexity and T...

This note describes the fundamental algorithms of Elliptic Curve Cryptography (ECC) as they were defined in some seminal references from 1994 and earlier. These descriptions may be useful for implementing the fundamental algorithms without using any of the specialized methods that were developed in following years. Only elliptic curves defined over fields of characteristic greater than three ar...