Cayley-Purser algorithm

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The Cayley-Purser algorithm was published in early 1999 by Irishwoman Sarah Flannery, who was sixteen years old at the time. She named the cryptographic algorithm for mathematician Arthur Cayley and Michael Purser, founder of Baltimore Technologies, a Dublin data security company.

During a work-experience placement with Baltimore Technologies, Sarah was shown an unpublished paper by Michael Purser which outlined a new public-key cryptographic scheme using non-commutative multiplication. She was asked to write an implementation of this scheme in Mathematica as part of her duties during her placement.

Before this placement, Sarah had attended the 1998 ESAT Young Scientist and Technology Exhibition with a project describing already existing crytographic techniques from Caesar cipher to RSA. This had won her the Intel Student Award which included the opportunity to compete in the 1998 Intel International Science and Engineering Fair in the United States. Feeling that she needed some original work to add to her exhibition project, Sarah asked Michael Purser for permission to include work based on his cryptographic scheme.

On advice from her mathematician father, Sarah decided to use matrices to implement Purser's scheme as matrix multiplication has the necessary property of being non-commutative. As the resulting algorithm would depend on multiplication it would be a great deal faster than the RSA algorithm which uses an exponential step. For her Intel Science Fair project Sarah prepared a demonstration where the same plaintext was enciphered using both RSA and her new Cayley-Purser algorithm and it did indeed show a significant time improvement.

Returning to the ESAT Young Scientist and Technology Exhibition in 1999, Sarah expanded further on the new material she had been working on. She formalised the estimated time the new algorithm would take in comparison to RSA to add to the empirical data from running them against each other. She also attempted to determine whether the new algorithm was vulnerable to any attacks which would make it easy to break. To achieve this she had to do a comprehensive investigation of possible attacks and had found none which worked.

Sarah did not make any claims that the Cayley-Purser algorithm would definitely replace RSA, knowing that any new cryptographic system would need to stand the test of time before it could be acknowledged as a secure system. The media were not so circumspect however and when she received first prize at the ESAT exhibition, newspapers around the world reported the story that a young girl genius had revolutionised cryptography.

In fact an attack on the algorithm was discovered shortly afterwards but she analyzed it and included it as an appendix in later competitions, including a Europe-wide competition in which she won a major award, acknowledging that the work she had done on this algorithm was just as impressive whether or not it resulted in a genuinely secure encipherment system.