Pollard's kangaroo algorithm: Difference between revisions

Revision as of 21:59, 21 October 2007

Revision as of 22:00, 21 October 2007

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5. Stop computing terms of <math>\{y_i\}</math> and <math>\{d_i\}</math> when either of the following conditions are met:

:A <math>y_iy_j = x_N</math> for some <math>j</math>. If the sequences <math>\{x_i\}</math> and <math>\{y_j\}</math> "collide" in this manner, then we have:

::<math>x_N = y_j \Rightarrow \alpha^{b+d} = \beta\alpha^{d_j} \Rightarrow \beta = \alpha^{b+d-d_j} \Rightarrow x \equiv b+d-d_j \pmod{p}</math>

:and so we are done.