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bmatrix environment simpler; the matrices are not equal, but equivalent under mod 5; s/-/−/ |
commutative property, not some inverse thing |
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{{Short description|1999 public-key cryptography algorithm}}
{{One source|date=October 2019}}
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[[algorithm]] published in early 1999 by 16-year-old [[Ireland|Irishwoman]] [[Sarah Flannery]], based on an unpublished work by [[Michael Purser]], founder of [[Baltimore Technologies]], a [[Dublin]] data security company.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.
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This group is chosen because it has large order (for large semiprime ''n''), equal to (''p''<sup>2</sup>−1)(''p''<sup>2</sup>−''p'')(''q''<sup>2</sup>−1)(''q''<sup>2</sup>−''q'').
Let <math>\chi</math> and <math>\alpha</math> be two such matrices from GL(2,''n'') chosen such that <math>\chi\alpha
:<math>\beta = \chi^{-1}\alpha^{-1}\chi,</math>
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{{DEFAULTSORT:Cayley-Purser algorithm}}
[[Category:Public-key encryption schemes]]
[[Category:Broken cryptography algorithms]]
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