An implementation of ElGamal elliptic curves cryptosystems (original) (raw)

IMPLEMENTATION OF ELLIPTIC - CURVE CRYPTOGRAPHY

IAEME Publication, 2020

Elliptic curve cryptography (ECC) is a procedure to generate public key between two distant partners namely, Alice and Bob used in public key cryptography. This method is based on the algebraic structure of elliptic curves over finite fields. ECC is important in the sense that it involve keys of smaller length in comparison to other non-Elliptic curve cryptography to provide equivalent security. During this work, we implement an algorithm in python programming language to generate public key using the method of ECC.

IJERT-An Implementation Of Elliptic Curve Cryptography

International Journal of Engineering Research and Technology (IJERT), 2013

https://www.ijert.org/an-implementation-of-elliptic-curve-cryptography https://www.ijert.org/research/an-implementation-of-elliptic-curve-cryptography-IJERTV2IS1419.pdf The internet is slowly becoming an increasingly dangerous mode of communication for all forms of highly sensitive data. The increased dependency by individuals, institutions and corporations over the Internet to carry out critical business processes have provided a playing field for the intruders to carry out different attacks on the system and on the network. The security to critically confidential information such as personal identity information, credit card details, online transactions and e-commerce is the need of the hour which depends on top of cryptography. It is thought that RSA is a very secure cryptography algorithm and almost all software products provide advanced data encryption are designed over it. The bit length for RSA has increased over the years to make the encryption very tough, which increases the processing time and storage requirement is the real concern for today. The objective of this paper is to propose an alternative algorithm for cryptography based on mathematical objects known as elliptic curves. The proposed algorithms provide a better security with shorter bit length than RSA. Hence elliptic curve cryptography is the only solution today where better security can be achieved with a smaller key size thereby reducing the processing overhead.

An Enhanced Elliptic Curve Cryptosystem for Securing Data

International Journal of Computer Applications, 2018

The purpose of this research is to enhance the cryptographic system called the Elliptic Curve. Elliptic Curve cryptosystem (ECC) is a technique of public-key encryption, which is rooted on the arithmetical construction of elliptic curves over finite fields. Elliptic Curve Cryptographic System necessitates smaller keys compared to non-ECC cryptography to offer equal security. The security of RSA is based on the computational task of considering extensive numbers leading to an increase in encryption computation time, slower connection of the SSL handshake and increase in CPU usage during handshakes. Therefore, there should be a new way of solving this problem, which is ECC encryption. Elliptic curves are effective for digital signatures, key agreement, generators, pseudo-random and other related tasks. The first phase of the project involves understanding the key exchange of Diffie-Hellman and applying the properties of the Elliptic Curves. It is terminated with key facts that the Elliptic Curve Cryptography has a shorter key length, saves bandwidth, which facilitates key generation during the encryption/decryption of data, also the assurance of faster encryption and decryption, and notwithstanding its efficiency and efficacy in small devices.

Public Key Cryptosystems RSA and ElGamal : A Technical Report

Technical Report of National Institute of Science and Technology (NIST), India, Summer Research Program, 2013 , 2013

To overcome the problems faced in symmetric key algorithms, people have chosen Asymmetric Key algorithms for communication. Communication with Asymmetric algorithms will give us transmission of information without exchanging the key. Public-key cryptography refers to a cryptographic system requiring two separate keys, one of which is secret and one of which is public. Public-key cryptography is widely used. It is an approach used by many cryptographic algorithms and cryptosystems. It underpins such Internet standards as Transport Layer Security (TLS), PGP, and GPG. RSA and Diffie–Hellman key exchange are the most widely used public key distribution systems, while the Digital Signature Algorithm is the most widely used digital signature system. In this report we are mainly concentrating on some asymmetric algorithms which are mostly used. They are RSA cryptosystem and ElGamal Cryptosystem. It also gives brief mathematical explanations. The RSA algorithm is the most commonly used encryption and authentication algorithm and is included as part of the Web browsers from Microsoft and Netscape.RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem.. The RSA algorithm involves three steps: key generation, encryption and decryption. In this we mainly concentrate on algorithms for Primality Testing, Extended Euclidian’s algorithm, Modular Exponentiation solving algorithm, etc. ElGamal System is a public-key cryptosystem based on the discrete logarithm problem. It consists of both encryption and Signature algorithms. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm. In this we concentrate on the algorithms Cyclic Groups, Modular Exponentiation solving algorithms etc.

On Elliptic Curves Cryptography Council for Innovative Research INTRODUCTION

2013

Elliptic curve cryptography is an asymmetric key cryptography. The points on two dimensional elliptic curve are used for declaration of data encryption & decryption. It include public key generation on the elliptic curve and private key generation to decrypt the data. The present paper deals with an overview of Elliptic curve cryptography (ECC) and its implementation through coordinate geometry for data encryption. We introduce a new approach in the form of cardan's method to find points on X axis at elliptic curve over finite field and form public key cryptographic system and finally we define two dimensional alphabetic table and description in the form of algorithm to use it for plain text encryption.

The comparison of several cryptosystems using the elliptic curve: a report

International Journal of Electrical and Computer Engineering (IJECE), 2024

The elliptic curve cryptosystem (ECC) has several applications in Information Security, especially in cryptography with two main activities including encrypting and decrypting. There were several solutions of different research teams which propose various forms of the elliptic curve cryptosystem on cryptographic sector. In the paper, we proposed a solution for applying the elliptic curve on cryptography which is based on these proposals as well as basic idea about the elliptic curve cryptosystem. We also make comparison between our proposal and other listed solution in the same application of the elliptic curve for designing encryption and decryption algorithms. The comparison results are based on parameters such as time consumption (t), RAM consumption (MB), source code size (Bytes), and computational complexity.

A Detailed Study of Elliptic Curve Cryptography Algorithm and Its Performance.

International Journal of Engineering Sciences & Research Technology, 2013

In this paper, we propose a detailed study of Elliptic Curve Cryptography Algorithm and its performance..ECC can be used with fewer keys to give more security, high speed in a less bandwidth. While these advantages make ECC propose for mobile devices, they can provide computational burden on secure web servers. In resource constrained system, Elliptic Curve Cryptography is a promising alternative for public algorithms, because it provides similar level of security with proposed shorter keys than conventional integer based public key algorithm. ECC over binary field is taken up with special interest because the operation in binary filed operation, are thought to be more in space and efficient in time. However, the software implementation of ECC over binary field are still slow, especially on low end processors, which are used in small computing devices such as sensors node, mobile phone, etc. This proposed paper, studied the Cryptography algorithms and software implementation of ECC. Firstly, while implementing ECC with software, the choice of some architectural parameters like word size may affect the choice of algorithms or not, has been examined. Also, identification of software for low-end processors has been done. In addition, this paper has examined several implements to the instruction that architecture of an 8 bit processor and studied their impact on the performance of ECC with other algorithms. ECC is well is well suited for high speeds, lower power consumption, bandwidth savings, storage efficiencies, smaller certificates and it reduces computational time and also the amount of data transmitted and stored, and strong security for low-power devices in wireless networks.

An implementation of the El Gamal elliptic curve cryptosystem ove

Since the earliest times, individuals and groups of individuals have been interested in communicating sensitive information in a manner which would guarantee that such information could not be arbitrarily received. Further, such information was to be received by select recipients and this required that a means of secure information transmission be found and employed. To these ends, methods of information encryption have ever since been sought and employed. The entire study and practice of this activity, cryptology, the science of message encryption and decryption, provides a framework for this thesis. In particular, the development of cryptology has been influenced by some specific areas of mathematics, employing abstract mathematical concepts and utilizing algebraic structures known as elliptic curves. It is with respect to these structures and their utilization in specific cryptosystems, called elliptic curve cryptosystems on which this thesis focuses. More specifically, this thesis is concerned with the implementation of such a cryptosystem and is a demonstration of that implementation. Additional pertinent examples, illustrations and supporting computer programs are included to present a self-contained work.

Modified ElGamal Elliptic Curve Cryptosystem using Hexadecimal Representation

Indian Journal of Science and Technology, 2015

Data encryption is an important issue and widely used in recent times to protect the data over internet and ensure security. One of the mostly used in public key cryptographies is the Elliptic Curve Cryptography (ECC). A new modified method has been proposed to encrypt / decrypt data using ECC in this paper. This modification converts each character of the plaintext message to its hexadecimal ASCII value of two digits, then separates the value into two values. After that, the transformation is performed on each value into an affine point on the Elliptic Curve E. This transformation is used to modify ElGamal Elliptic Curve Cryptosystem (EGECC) to encrypt / decrypt the message. In modified method, the number of doubling and adding operations in the encryption process has been reduced. The reduction of this number is a key point in the transformation of each character into an affine point on the EC. In other words, the modified method improved the efficiency of the EGECC algorithm. Moreover, using the hexadecimal ASCII value makes EGECC more secure and complicated to resist the adversaries.