BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Brett Stevens and Lucas Perin (Carleton University and Federal Uni versity of Santa Catarina) DTSTART:20210805T160000Z DTEND:20210805T170000Z DTSTAMP:20260416T224653Z UID:CCM2021/2 DESCRIPTION:Title: Randomness properties of $\\mathbb{Z}_v$ ElGamal sequences\nby Brett S tevens and Lucas Perin (Carleton University and Federal University of Sant a Catarina) as part of Carleton Combinatorics Meeting 2021\n\n\nAbstract\n In 2020 Boppré et al. investigated the randomness properties of the ElGam al function considered as a permutation $x \\to g^x$ on $\\mathbb{Z}_{p}^ *$. They prove that the graph of this map is equidistributed and demonstr ate experimentally that this map behaves like a random permutation with re spect to the number of cycles and the number of $k$-cycles. These randomne ss properties imply that cryptographic systems based on ElGamal are resist ant to certain attacks and they call for investigation of other randomness properties. We investigate the randomness properties of $\\mathbb{Z}_v$ sequences derived from ElGamal. We prove that the period and number of oc currences of runs and tuples match sequences from random permutations clos ely. We describe extensive experiments which probe these similarities furt her.\n LOCATION:https://researchseminars.org/talk/CCM2021/2/ END:VEVENT END:VCALENDAR