Role of Prime Numbers in Cryptography
DOI:
https://doi.org/10.29070/ddy24369Keywords:
Prime numbers, RSA algorithm, public key cryptography, number theory, data security, modular arithmeticAbstract
The significance of prime numbers is profound within the domain of cryptography. In recent times, with the advent of digital communication systems, there is a need for the security of messages being transmitted in various fields like banking, e-commerce, government communications, and even personal matters. The field of cryptography is based on problems that are simple to solve in one direction but complex to solve in the other direction. Prime numbers are such examples, especially when large composite numbers are involved.
This paper explores the theoretical and practical role of prime numbers in modern cryptographic systems. This paper commences with basic mathematical concepts regarding prime numbers, which include the Fundamental Theorem of Arithmetic and modular arithmetic.
Next, it elaborates upon the use of these theories in public key encryption through an example of the RSA algorithm. Mathematical formulae are used alongside examples and visual aids to explain the process. Apart from discussing practical applications of prime numbers like internet security, digital signatures, and Blockchain technology, certain challenges are also presented. From the findings, it is evident that the prime number is a critical tool for secure communication in the digital age and will remain an active field of research in mathematics and computer science.
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