Sarah's cracking algorithm

K.E.M. Share this page
January 1999

Sarah Flannery, a student at Scoil Mhuire Gan Smal in Blarney, Co. Cork, was awarded an Intel Fellows Achievement Award for her project in the Chemical, Physical and Mathematical Category at the 1998 Esat Telecom Young Scientist and Technology awards.

Sarah's project for the exhibition was entitled "Cryptography - The Science of Secrecy". Working with matrices and using her PC at home for experiments, Sarah developed and tested a new cryptography algorithm for encrypting data. While the work has been around for a little while, media attention has recently skyrocketed!

The initial idea for the algorithm was developed while Sarah was on a placement at Baltimore-Zergo in Dublin, and she has called it the Cayley-Purser algorithm, named after Arthur Cayley, an 19th-century Cambridge mathematician, and Michael Purser, a cryptographer who inspired her.

Sarah's new algorithm is a competitor to the popular RSA algorithm. Where RSA uses exponentiation to encode and decode a message, Cayley-Purser uses matrix multiplication. This means that while RSA grows as a cubic with the length of the encryption "key", Cayley-Purser grows quadratically. For a typical key length of 1024 bits, this makes Cayley-Purser around 75 times faster.

One downside of Sarah's algorithm is that the encrypted messages it produces are much longer than those produced by RSA. More significantly, however, there is still some possibility that Cayley-Purser might have some "security holes", making it too easy to "crack the code". Now that Sarah and her algorithm are receiving so much attention, other researchers will begin to explore the security properties of Cayley-Purser, and see how it stacks up against the dominant RSA.

What's going on?
Some Internet discussion of Sarah's work.
The homepage of RSA.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.