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Before this placement, Sarah had attended the 1998 [[Young Scientist and Technology Exhibition|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.
Sarah, on advice from her father, decided to use [[Matrix (mathematics)|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 then the [[RSA]] algorithm which uses an [[exponent|exponential]] step. For her Intel Science Fair project Sarah prepared a demonstration where the same plaintext
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 rather than merely running them against each other and she had 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 survey of possible attacks and had found none which worked.
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