An Encryption and Decryption More Secure Elgamal Cryptosystem

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.

International Journal of Computers and Applications, 2019

ElGamal Cryptosystem (EC) is a non-deterministic scheme which produces different outputs for the same input, making the cryptosystem more secure. On the other hand, the efficiency of its cryptosystem is low as it produces a 2:1 expansion in size from plaintext to ciphertext, resulting in a delay in execution time. Therefore, this paper presents a Modified ElGamal Cryptosystem (MEC) to increase the efficiency by speeding up the execution time and reducing the expansion rate in the file size after the encryption process. A comparison between the proposed MEC and the traditional EC is carried out using the same programming environment, and the implementation is tested using text data of different sizes. The results show that the performance of the proposed MEC is better than the traditional EC in terms of execution time and expansion rate. Whereas, the security of the proposed MEC is analogous to the traditional EC, which is based on the difficulty of solving the discrete logarithm problem.

2017

Data security is of utmost importance in today’s world. Especially when the data is travelling through an insecure communication network. Cryptography addresses the necessary elements for secure communication such as privacy, confidentiality, key exchange, authentication and non-repudiation. There are symmetric key encryption techniques which use only one key for both encryption and decryption of the data. . On the other hand, there are asymmetric key based algorithms which use a pair of keys, one for encryption, and the other for decryption, whose security is higher as compared to the symmetric. In this paper a hybrid asymmetric cryptosystem algorithm will be implemented which combine the methods RSA and El-gamal. The hybrid cryptosystem that improve the security and performance will be based on encryption time , decryption time and throughput.

Journal of Discrete Mathematical Sciences and Cryptography

The ElGamal cryptosystem is one of the most widely used public-key cryptosystems that depends on the difficulty of computing the discrete logarithms over finite fields. Over the years, the original system has been modified and altered in order to achieve a higher security and efficiency. In this paper, a generalization for the original ElGamal system is proposed which also relies on the discrete logarithm problem. The encryption process of the scheme is improved such that it depends on the prime factorization of the plaintext. Modular exponentiation is taken twice during the encryption; once with the number of distinct prime factors of the plaintext and then with the secret encryption key. If the plaintext consists of only one distinct prime factor, then the new method is similar to that of the basic ElGamal algorithm. The proposed system preserves the immunity against the Chosen Plaintext Attack (CPA).

Circuits and Systems, 1998. …, 1999

Concept of public key cryptography was first introduced by Difie and Hellman in 1976 which using discrete logarithm problem as base of dificulty. In 1985, T. ElGamal proposed public key cyptosystem scheme based on discrete logarithm problem. Elliptic curve cryptosystems were first proposed in 1985 independently by Neil Koblitz and Victor Miller. Elliptic curve cryptosystems are unique in using elliptic curve groups for arithmetic. This cryptosystem based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm problem in an elliptic curve group appears to be much harder than the discrete logarithm problem in other groups. Hence elliptic curwes cyptosystem can match the security of other cryptosystems while wing smaller key. In this paper we will discuss a VLSI implementation of Elliptic Curves Cryptosystem for ElGamal encryption scheme.

International Journal of Computing and Engineering

Purpose: In this research, a comparative analysis of the RSA and ELGAMAL algorithms is presented using their encryption and decryption speed with different key sizes. ElGamal and RSA are two popular public-key cryptographic algorithms that depend on the mathematical difficulty of computing discrete logarithms in finite fields and factoring large integers, respectively. Methodology: In this study, the speed at which messages of various sizes can be encrypted and decrypted using various key sizes is used to gauge how well these algorithms work. Findings: RSA usually outperforms ElGamal in terms of encryption and decryption speed, according to the results. However, as the key sizes grow, the performance gap between the two algorithms narrows. Unique Contribution to Theory, Policy and Practice: These findings can aid in selecting the appropriate algorithm and key size for different applications that require secure communication and data encryption.

2015

Cryptography is generated to create secure data transmission over networks. The algorithm chosen for cryptography should satisfy the conditions of authentication, confidentiality, integrity and non-repudiation. Recent years have witnessed the phenomenal growth of RSA. We design an algorithm to merge both enhanced RSA algorithm and El-Gamal algorithm to provide user with a higher level of data security. The enhanced RSA algorithm enables faster encryption and decryption process and generating public and private key faster than the original RSA. The Enhanced RSA Cryptosystem is based on Integer Factorization Problem (IFP), while the El-Gamal Cryptosystem is based on Discrete Logarithm Problem (DLP). This model works on the basis of combining IFP and DLP. The weaknesses of RSA algorithm when we use two prime‟s number are the following points which are used to break the algorithm in most cases. These weaknesses are: (a) Small encryption exponent, if you use a small exponent like e=3 and...

2014

Key distribution problem in symmetric cryptography has been solved by the emergence of asymmetric cryptosystem. Due to its mathematical complexity, computation efficiency becomes a major problem in the real life application of asymmetric cryptosystem. This scenario encourage various researches regarding the enhancement of computation efficiency of asymmetric cryptosystems. ElGamal cryptosystem is one of the most established asymmetric cryptosystem. By using proper parameters, ElGamal cryptosystem is able to provide a good level of information security. On the other hand, Compression-Crypto technique is a technique used to reduce the number of plaintext to be encrypted from plaintext become only 2 plaintext. Instead of encrypting plaintext, we only need to encrypt these 2 plaintext. In this paper, we embed the Compression-Crypto technique into the ElGamal cryptosystem. To show that the embedded ElGamal cryptosystem works, we provide proofs on the decryption processes to recover the encrypted plaintext.

International Journal of Computer Applications, 2020

An increase in network technology development has its own downside; thus as more connections are established with various global computer networks daily, the more exposed the connected systems are to unauthorized access, thus making security of data very important to address. Internet based transaction applications such as internet banking, online shopping, etc., involves sharing of very sensitive information between two or more parties that should be confidential. This requires very secure end-to-end connections that will ensure the data integrity, confidentiality, authenticity, etc. Cryptography is one of the most reliable and best, if not the best way to keep sensitive data from unauthorized users. This implies a good cryptosystem that maximizes security of the information been transferred and minimizes a substantial amount of delay time is needed. This is dependent on the particular cryptosystem one chooses to secure information. Also of the two known types of cryptosystems, the best in security is asymmetric cryptosystems, which uses two different keys; one for encryption and the other for decryption, whiles symmetric cryptosystems use the same key for both encryption and decryption. The essential features of asymmetric cryptosystems that determines their efficiency and security are; encryption computation time, decryption computation time, performance, encryption throughput, decryption throughput, throughput, randomness, key length and Operation per Instruction (O/I). This research seeks to examine these properties of some asymmetric cryptosystems and subsequently develop a proposed cryptosystem that is more secure and efficient. The results of this research clearly demonstrate that, the proposed cryptosystem has better results for all the properties stated above.

International Journal of Information and Communication Technology, 2018

In this paper, we propose a new and practical variant of ElGamal encryption which is secure against every passive and active adversary. Under the hardiness of the decisional Diffie-Hellman assumption, we can prove that the proposed scheme is secure against an adaptive chosen ciphertext attacks in the standard model. Such security verifies not only the confidentiality but also verifies the integrity and the authentication of communications. We display that the modified scheme furthermore achieves anonymity as well as strong robustness.