Cayley–Purser algorithm: Difference between revisions

Revision as of 03:36, 5 February 2008

Revision as of 03:37, 5 February 2008

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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 <math>\epsilon</math> \pmod n</math>

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.