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Expand with a full discussion of the algorithm, overview of its security and flaw, and some rewriting for tone |
Note on its use as a hybrid private-key/public-key algorithm |
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The '''Cayley-Purser algorithm''' was a [[public-key cryptography]] [[algorithm]] published in early [[1999]] by 16-year-old [[Ireland|Irishwoman]] [[Sarah Flannery]], based on an unpublished work by [[Michael Purser]], founder of [[Baltimore Technologies]], a [[Dublin]] data security company.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.
== History ==
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However, the system was broken when a method for finding a multiple <math>\chi'</math> of <math>\chi</math> using the public parameters by solving the congruence:
:<math>\delta\left(\beta_{11}^{-1} - \alpha_{11}\right) \equiv
for <math>\delta</math>, where <math>\alpha_{11}, \beta_{11}</math> are the top-left elements of <math>\alpha, \beta</math>. Since any multiple of <math>\chi</math> can be used to decipher, this presents a fatal weakness for the system that has not yet been reconciled.
This flaw does not preclude the algorithm's use as a mixed private-key/public-key algorithm, if the sender transmits <math>\epsilon</math> secretly, but this approach presents no advantage over the common approach of transmitting a [[symmetric encryption]] key using a public-key encryption scheme and then switching to symmetric encryption, which is faster than Cayley-Purser.
== References ==
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