TIME AND SPACE COMPLEXITY ANALYSIS OF RSA AND ELGAMAL CRYPTOGRAPHIC ALGORITHMS ON MIXED DATA

ADENIYI, ABIDEMI EMMANUEL (2021) TIME AND SPACE COMPLEXITY ANALYSIS OF RSA AND ELGAMAL CRYPTOGRAPHIC ALGORITHMS ON MIXED DATA. Masters thesis, Landmark University, Omu Aran, Kwara State.

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Abstract

The complexity study of algorithms, especially computationally intensive ones is of great significance in the field of complexity. Cryptographic algorithms are considered to be computationally intensive because they utilize a substantial number of computational resources, such as CPU memory and processing time. Cryptographic algorithms provide a solution to the security of data transmission whereby ensuring integrity, confidentiality and authentication of any form of data. However, there are still challenges of which cryptographic algorithms are suitable in terms of computation speed and memory usage. Whereas, a good number of research efforts have been put into experimenting on the complexities of the cryptographic algorithm on text, image and audio data, little has been done on video data. In this study, the time and space complexity of RSA and ElGamal cryptographic algorithms on mixed data was carried out. RSA and ElGamal cryptographic algorithms was implemented using C-sharp (C#) programming language to encrypt and decrypt text, image, audio and video dataset. In achieving the objectives of the study, both the implemented algorithms (RSA and ElGamal) are depicted using pseudocodes and flowcharts, while some of the datasets used were sourced from various online repositories. The time complexities of each dataset was obtained using the CPU internal clock while the space usage for each operations on each of the dataset was obtained using the computer internal memory. Tables and graphs was used to carry out the comparative analysis of both algorithms. The time and space complexity of RSA and ElGamal algorithms were experimented on text, image, audio and video dataset. The experimental results revealed that RSA outperformed ElGamal in terms of computational time during encryption of all categories of data. ElGamal outperformed RSA in terms of computational time during decryption of all categories of data. ElGamal algorithm outperformed RSA in terms of memory usage during encryption of all categories of data while both algorithms used relatively the same amount of space during decryption of all categories of data used. Based on the comparative analysis of the time and space complexity on both RSA and ElGamal algorithms, it was discovered that RSA is a better algorithm when it comes to time complexity, that is, RSA can be said to be a time-efficient algorithm. ElGamal algorithm performed better than RSA in the memory usage aspect, therefore the ElGamal algorithm is said to be a memory-efficient algorithm. Therefore, this study hereby recommend that other measurement metrics may be used to compare both algorithms in future works.

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