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SUMMARY:Maciej Grześkowiak (University of A. Mickiewicz\, Poznań\, Polan
 d)
DTSTART:20260929T190000Z
DTEND:20260929T200000Z
DTSTAMP:20261019T010236Z
UID:gc-arithmetic-geometry/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/gc-arithmeti
 c-geometry/78/">Algorithmic Methods for Generating Primes for Cryptographi
 c Systems</a>\nby Maciej Grześkowiak (University of A. Mickiewicz\, Pozna
 ń\, Poland) as part of The Graduate Center Arithmetic Geometry Seminar\n\
 nLecture held in The Graduate Center - room 9116.\n\nAbstract\nThis talk d
 iscusses algorithmic methods for generating prime parameters used in crypt
 ographic systems based on finite abelian groups. The main objective is to 
 generate primes that allow the construction of groups containing large pri
 me-order subgroups while keeping the subgroup index small and ensuring com
 putational efficiency. We consider this problem for multiplicative groups 
 of finite fields\, elliptic curves over finite fields\, and pairing-friend
 ly elliptic curves. Particular attention is given to generating pairs of p
 rimes satisfying prescribed divisibility\, congruence\, and algebraic cond
 itions. We also discuss the complexity of the corresponding probabilistic 
 algorithms\, including expected polynomial-time results in several of thes
 e settings.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/78/
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