The use of elliptic-curve groups in cryptography, suggested by Miller [1] and Koblitz [2] three decades ago,provides the same level of security for the Discrete Logarithm Problem as multiplicative groups, with much smallerkey sizes and parameters. The idea was refined two years later by Koblitz, who worked with the group formed bythe points of the Jacobian of hyperelliptic curve...

The study of elliptic curves has historically been a subject of almost purely mathematical interest. However, Koblitz and Miller independently showed that elliptic curves can be used to implement cryptographic primitives [13], [17]. This thrust elliptic curves from the abstract realm of pure mathematics to the preeminently applied world of communications security. Public key cryptography in gen...

A formula for point addition in elliptic curves using a±ne representation and its implementation in FPGA is presented. The use of this new formula in hardware implementations of scalar multiplications for elliptic curve cryptography has the main advantages of: (i) reducing area for the implementations of elliptic curve point addition, and (ii) increasing the resistance to side channel attacks o...

The security of data encrypted with an encryption algorithm should be guaranteed such that it is never easy for a third party to recover the message from data. To this effect, ECC has been reliable option. However, base equation defines Elliptic Curve Cryptography (ECC) in form linear one unknown which solve. ease can solved weak point algorithm. Thus, aim research work improve by improving nat...

Smart Grids (SGs) are introduced as a solution for standard power distribution. The significant capabilities of smart grids help to monitor consumer behaviors and systems. However, the delay-sensitive network faces numerous challenges in which security privacy gain more attention. Threats transmitted messages, control over grid information user major concerns security. Providing secure communic...

Abstract Elliptic Curve Cryptography (ECC) is one of the strongest and most efficient cryptographic techniques in modern cryptography. This paper gives following introduction: The introduction cryptography’s development; elliptic curve; principle ECC; horizontal comparison between ECC other types cryptography; breakthrough applications by using a method literature review. study’s findings indic...

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...

With the explosion of networks and the huge amount of data transmitted along, securing data content is becoming more and more important. Data encryption is widely used to ensure security in open networks such as the Internet. With the fast development of cryptography research and computer technology, the capabilities of cryptosystems such as of RSA and Diffie-Hellman are inadequate due to the r...