Cayley–Purser algorithm

The Cayley–Purser algorithm was a public-key cryptography algorithm published in early 1999 by 16-year-old Irishwoman Sarah Flannery, based on an unpublished work by Michael Purser, founder of Baltimore Technologies, a Dublin data security company. Flannery named it for mathematician Arthur Cayley. It has since been found to be flawed as a public-key algorithm, but was the subject of considerable media attention.

During a work-experience placement with Baltimore Technologies, Flannery was shown an unpublished paper by Michael Purser which outlined a new public-key cryptographic scheme using non-commutative multiplication.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.

Before this placement, Flannery 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, Flannery asked Michael Purser for permission to include work based on his cryptographic scheme.

On advice from her mathematician father, Flannery 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 Flannery 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.

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