Cayley–Purser algorithm: Difference between revisions

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Key generation: let's arrange this in a reasonable way, with reasonable parameters, cleanly.
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\left[\begin{matrix}3 & 4 \\ 1 & 1\end{matrix}\right]</math>
 
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'').
 
:<math>n\phi(n)^2(p+1)(q+1)</math>
 
where <math>\phi</math> is [[Euler's totient function]].
 
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: