Cayley–Purser algorithm: Difference between revisions

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commutative property, not some inverse thing
 
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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^{-1} \not= \alpha\chi</math>. Choose some natural number ''r'' and compute:
 
:<math>\beta = \chi^{-1}\alpha^{-1}\chi,</math>