Abstract
We show a Birthday Paradox for self-intersections of Markovchains with uniform stationary distribution. As an application, we analyzePollard's Rho algorithm for finding the discrete logarithm in a cyclicgroup G and find that, if the partition in the algorithm is given by arandom oracle, then with high probability a collision occurs in Θ(√|G|)steps. This is the first proof of the correct bound which does not assumethat every step of the algorithm produces an i.i.d. sample from G.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.