Applications of Number Theory in Cryptography

Fundamentals of number theory are vital for the formation of modern cryptographic algorithms that assure secure communication and data privacy in many examples of practical use. Cryptographic algorithms based on the number theory which are already in practice include RSA and elliptic curve among others and are employed in securing online transactions, digital signatures and controlled access systems.

These algorithms use the intrinsic properties of prime numbers, modular arithmetic, and the discrete logarithm to encrypt confidential information, sign digital documents, and identify the users. In addition, principles of number theory like cryptographic hash functions help in successfully verifying data integrity and preventing tampering during digital documentation or even blockchain transactions.

Organizations and individuals can shield their digital properties and also their identities and communications from cyber-attacks and unauthorized access by applying number theory in cryptography.

Number theory, which is the branch of mathematics relating to numbers and the rules governing them, is the mother of modern cryptography – the science of encrypting communication. Cryptography algorithms that guarantee data privacy, integrity, and authenticity derive their base from number theory, which is utilized to ensure data confidentiality and integrity during online transactions and the identification of digital users.

In this article, we show where the number theory is used in real-life applications in cryptography and how it helps to keep the digital world safe against hackers and unwelcome guests.