The Key to Cryptography: The RSA Algorithm

Cryptography is the study of codes, as well as the art of writing and solving them. It has been a growing area of study for the past 40 years. Now that most information is sent and received through the internet, people need ways to protect what they send. Some of the most commonly used cryptosystems today include a public key. Some public keys are based around using two large, random prime numbers combined together to help encrypt messages. The purpose of this project was to test the strength of the RSA cryptosystem public key. This public key is created by taking the product of two large prime numbers. We needed to find a way to factor this number and see how long it would take to factor it. So we coded several factoring algorithms to test this. The algorithms that were implemented to factor are Trial Division, Pollard’s Rho, and the Quadratic Sieve. Using these algorithms we were able to find the threshold for decrypting large prime numbers used in Cryptography.