Aplikasi Teorema Fermat dalam Kriptografi
DOI:
https://doi.org/10.22437/msa.v5i1.38094Keywords:
Fermat's theorem, Cryptography, RSA algortihmAbstract
Cryptography is the science and technique of disguising messages in a unique form so that they can only be read and processed by the intended recipient. Many studies have been conducted to develop algorithms that can be used to encode information in a way that is difficult to crack and cannot be recognized by adversaries. One example of the most popular algorithms is the Rivest-Shamir-Adleman (RSA), which uses different key pairs for the encryption and decryption process of messages, usually known as the public key and private key. In public key-based encryption systems such as RSA, Fermat's theorem plays an important role because it enables modular exponential calculations on key pairs to be performed efficiently and provides a security basis for the RSA algorithm. Thus, this research aims to describe the application of Fermat's theorem in the RSA algorithm, where the encryption and decryption process involves modular exponentiation with public and private keys. As a result, using the properties of modular exponentiation in Fermat's theorem, this system ensures information remains secure from attacks by third parties without access to the private key, even if they succeed in intercepting encrypted messages. It can be concluded that Fermat's theorem plays a crucial role in establishing a solid mathematical foundation for creating secure and efficient cryptographic systems.
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