A Comparative Study of RSA and ELGAMAL Cryptosystems

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.

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.

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" ...

Due to its speed, spread and ease of use, the internet has now become a popular means through which useful data and information are transported from one location to another. This shift in the way data and information is being transported then calls for a new or different approach to security issues to save data in-transit from hackers. Cryptography is one of the approaches that have been explored for data security on the internet. RSA and El-Gamal (based on concepts of discrete logarithm) cryptographic algorithms are mostly employed to handle data security on the internet. This research work present a fair comparison between RSA and Discrete Logarithm algorithms along this direction; efficiency (time and space) by running several encryption setting to process data of different sizes. The efficiency of these algorithms is considered based on key generation speed, encryption speed, decryption speed, and storage requirement of the cipher text. In this paper, simulation has been conducted using Java programming language. Texts of different sizes were encrypted and decrypted using RSA and El Gamal during the testing. Based on the result of the simulation, El Gamal is faster than RSA in terms of key generation speed but consumes more memory space than RSA. RSA is faster than El Gamal in terms of encryption and decryption speed.

2018

This paper presents a performance study and analysis of two popular public-key cryptosystems: RSA with its two variants, and ECC (Elliptic Curve Cryptography). RSA is considered as the first generation public-key cryptography, which is very popular since its inception while ECC is gaining its popularity recently. Besides studying and analyzing the paper also suggests the supremacy among these cryptosystems based on the experimentation. The paper shows the result of the experimentation performed using these cryptosystems with the different modulus/key sizes recommended by the NIST. The modulus/key sizes are used such as 1024/2048/3072-bit for RSA and 160/224/256-bit for ECC. After experimentation and execution of these cryptosystems, the paper concludes that an ECC-based cryptosystem is better than an RSA or its variants-based cryptosystem, and an ECC based cryptosystem best suits for memory-constrained devices, as an ECC-based cryptosystem requires fewer resources than an RSA-based ...

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...

TELKOMNIKA (Telecommunication Computing Electronics and Control)

Cryptography is a growing science of data security. The integrity of a data is an important thing to keep the secrets contained in the data. In this research will be visualized the efficient quantities that use elliptic curves and do not use them. The Elgamal method is an asymmetric cryptographic algorithm whose complexity of processes. It is especially for digital signatures. This research will discuss about the use of ECC to optimize and streamline the Encryption and Decryption process in particular 128-bit Elgamal method. The hope is that by using elliptic curves the timing of the encryption and decryption process can run faster in the computation of Elgamal Method.

TELKOMNIKA Telecommunication Computing Electronics and Control, 2018

Cryptography is a growing science of data security. The integrity of a data is an important thing to keep the secrets contained in the data. In this research will be visualized the efficient quantities that use elliptic curves and do not use them. The Elgamal method is an asymmetric cryptographic algorithm whose complexity of processes. It is especially for digital signatures. This research will discuss about the use of ECC to optimize and streamline the Encryption and Decryption process in particular 128-bit Elgamal method. The hope is that by using elliptic curves the timing of the encryption and decryption process can run faster in the computation of Elgamal Method.

Lecture Notes in Computer Science, 2000

We present an attack on plain ElGamal and plain RSA encryption. The attack shows that without proper preprocessing of the plaintexts, both ElGamal and RSA encryption are fundamentally insecure. Namely, when one uses these systems to encrypt a (short) secret key of a symmetric cipher it is often possible to recover the secret key from the ciphertext. Our results demonstrate that preprocessing messages prior to encryption is an essential part of both systems.

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.