# A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm

@inproceedings{Kim2008ABP, title={A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm}, author={Jeong Han Kim and Ravi Montenegro and Yuval Peres and Prasad Tetali}, booktitle={ANTS}, year={2008} }

- Published 2008 in ANTS
DOI:10.1007/978-3-540-79456-1_27

We show a Birthday Paradox for self-intersections of Markov chains with uniform stationary distribution. As an application, we analyze Pollard’s Rho algorithm for finding the discrete logarithm in a cyclic group G and find that if the partition in the algorithm is given by a random oracle, then with high probability a collision occurs in ( √|G|) steps. Moreover, for the parallelized distinguished points algorithm on J processors we find that ( √|G|/J ) steps suffices. These are the first proofs… CONTINUE READING

Highly Cited

This paper has 31 citations. REVIEW CITATIONS

#### From This Paper

##### Topics from this paper.

17 Citations

23 References

Similar Papers