Lark Kim Implementing and Cracking the RSA Cryptosystem

The primary goal of our project is to implement the RSA cryptosystem in Maple 8. Our implementation includes finding primes suitable for RSA, translating text messages into blocks of large numbers and back, as well as encrypting and decrypting the numerical blocks. We found that our program could quickly encrypt long messages using primes with at least 512 bits and was capable of encrypting messages in a reasonable amount of time using 1024bit primes. According to the RSA website (www.rsasecurity.com) 1024-bit primes are still considered safe for everyday use. In fact, they offer a $200,000 reward for the factorization of a certain 2048-bit composite. The next section of this paper will serve as a quick review of RSA. In section 3, we discuss the various properties that prime numbers should have for secure encryption as described in [4], [2], and [3]. We follow the method of [2] for generating these so-called strong primes. The final section of the paper discusses some methods for factoring n when p and q are not strong primes. The factorization algorithms we programmed were Pollard’s p−1 method and William’s p+ 1 method, taken from [6] and [7] respectively.