Public Key Cryptosystems RSA and ElGamal : A Technical Report

An asymmetric algorithm is an encryption technique that uses different keys on the process of encryption and decryption. This algorithm uses two keys, public key, and private key. The public key is publicly distributed while the private key is kept confidentially by the user and this key is required at the time of the decryption process. RSA and ElGamal are two algorithms that implement a public key cryptosystem. The strength of this algorithm lies in the bit length used. The degree of difficulty in RSA lies in the factorization of large primes while in ElGamal lies in the calculation of discrete logarithms. After testing, it is proven that RSA performs a faster encryption process than ElGamal. However, ElGamal decryption process is faster than RSA. Both of these algorithms are cryptographic public-key algorithms but have functions in different ways. RSA is a deterministic algorithm while ElGamal is a probabilistic algorithm.

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.

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 Science Technology & Engineering

Encryption and Decryption are two fundamental approaches in network security and cryptography. Both of these tools or we can say techniques are most commonly used nowadays. If we want to perform secure communication between sender and receiver than encryption and decryption are very useful. For this purpose, public key cryptography and private key cryptography is used. Here we present, we present an overview of the existing cryptographic system and will see some of the problems that arise in the existing cryptosystem. Then after we present the proposed system and provide advantages and implementation of our proposed system.

Information & Security: An International Journal, 2019

A R T I C L E I N F O : RECEIVED: 08 mar 2018 REVISED: 10 Nov 2018 ONLINE: 12 FEB 2019 K E Y W O R D S : Public Key Cryptography, Elliptic Curves, Discrete Logarithm Problem, ElGamal digital signature Creative Commons BY-NC-SA 4.0 Introduction Most of the historians consider that the public key cryptography appears for the first time in 1976 when Diffie and Hellman published their seminar paper “New directions in cryptography.” A method to obtain a common key between two partners who communicate over a public insecure channel was described. It was based on the hardness of the famous discrete logarithm problem. In 1978 Rivest, Shamir and Adleman proposed an algorithm to encrypt and decrypt confidential messages. The technical security relies mainly on hard mathematical problems in number theory and particularly on integer factorization. Until now, their Marouane Ihia & Omar Khadir, ISIJ 42 (2019): 117-126 118 discovery is considered as the most important and practical way to protect ...

2006 World Automation Congress, 2006

A powerful and practical public-key and digital signature scheme was produced by ElGamal. ElGamal public-key and digital signature scheme were modified from the domain of natural integers, Z, to the domains of Gaussian integers, Z[i], and polynomials over finite fields, F [x]. We implement the classical and modified ElGamal digital signature scheme to compare and to test their functionality, reliability and security. To test the security of the algorithms we use a famous attack algorithm called Baby-Step-Giant algorithm which works in the domain of natural integers. We enhance the Baby-Step-Giant algorithm to work with the modified ElGamal digital signature algorithms.

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.

2019

Computer and network security system are needed to protect data during their transmissions and to guarantee that data are authentic. Cryptography is useful not only for proving data to be secure but also for ensuring that data have not altered. So, it is needed to implement the public key cryptosystem in computer and network security system. In cryptography, symmetric key cryptosystems are faster than public key asymmetric cryptosystems. But public key cryptosystems are more secure than symmetric key cryptosystems and widely used in computer and network security system. This describes the comparison of RSA Rivest, Shame, Adelman public key cryptosystem and ElGamal public key cryptosystem. RSA public key cryptosystem is faster than ElGamal in encryption and decryption. This paper also describes the encryption decryption time comparison of RSA and ElGamal. Kyaw Myo Thu | Kyaw Swar Hlaing | Nay Aung Aung "Time Performance Analysis of RSA and Elgamal Public-Key Cryptosystems" ...

arXiv: Group Theory, 2019

In this paper, we propose two cryptosystems based on group rings and existing cryptosystem. First one is Elliptic ElGamal type group ring public key cryptosystem whose security is greater than security of cryptosystems based on elliptic curves discrete logarithmic problem (ECDLP). Second is ElGamal type group ring public key cryptosystem, which is analogous to ElGamal public key cryptosystem but has comparatively greater security. Examples are also given for both the proposed cryptosystems.