This worksheet is a talk given by John Cosgrave at the Annual International Conference on Technology in Collegiate Mathematics in 2003. In this, he explains the difference between private- key and public-key cryptography, demonstrate the Pohlig-Hellman private-key cryptographic method, demonstrate a simplified element of the renowned Rivest-Shamir-Adleman (RSA) public-key cryptographic method, and illustrate the relevance of the unsolved fast factorisation problem to the security of the RSA method.