A generalization of the ElGamal public-key cryptosystem
Rajitha Ranasinghe independent.academia.edu
A generalization of the ElGamal public-key cryptosystem
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.

Abstract: One of the classical problems in mathematics is the Discrete Logarithm Problem (DLP).The difficulty and complexity for solving DLP is used in most of the cryptosystems. In this paper we design a public key system based on the ring of polynomials over the field 𝐹𝑝 is developed. The security of the system is based on the difficulty of finding discrete logarithms over the function field 𝐹𝑝𝑛 with suitable prime p and sufficiently large n. The presented system has all features of ordinary public key cryptosystem. Keywords: Discrete logarithm problem, Function Field, Polynomials over finite fields, Primitive polynomial, Public key cryptosystem.

In this chapter, the authors have defined a new ElGamal cryptosystem by using the power Fibonacci sequence module m. Then they have defined a new sequence module m and the other ElGamal cryptosystem by using the new sequence. In addition, they have compared that the new ElGamal cryptosystems and ElGamal cryptosystem in terms of cryptography. Then the authors have defined the third ElGamal cryptosystem. They have, particularly, called the new system as composite ElGamal cryptosystem. The authors made an application of composite ElGamal cryptosystem. Finally, the authors have compared that composite ElGamal cryptosystem and ElGamal cryptosystem in terms of cryptography and they have obtained that composite ElGamal cryptosystem is more advantageous than ElGamal cryptosystem.

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.

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.

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...

In this paper, we present a new public key scheme which is a combination of RSA variant namely the Dependent-RSA (DRSA) and the general formulation of DGDLP. The security of this scheme depend equally on the integer factorization of n and the discrete logarithm on Zn, where n is a product of two large primes and Zn is the multiplicative group modulo n. The scheme is a randomized algorithm and it is at least as secure as the DRSA and ElGamal schemes.