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The number of solutions depends on |Cent(χ)|, which depends on the order of χ, since <χ> <= Cent(χ). |
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== Security ==
Recovering the private key <math>\chi</math> from <math>\gamma</math> is computationally infeasible, at least as hard as finding square roots mod ''n'' (see [[quadratic residue]]). It could be recovered from <math>\alpha</math> and <math>\beta</math> if the system <math>\chi\beta = \alpha^{-1}\chi</math> could be solved, but the number of solutions to this system is large as long as
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:
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