Generating a Large Prime Factor of p4 ± p2 + 1 in Polynomial Time

Authors:
Maciej Grześkowiak
Affiliations:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland 61-614
Venue:
OTM '08 Proceedings of the OTM 2008 Confederated International Conferences, CoopIS, DOA, GADA, IS, and ODBASE 2008. Part II on On the Move to Meaningful Internet Systems
Year:
2008

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Abstract

In this paper we present a probabilistic polynomial-timealgorithm for generating a large prime p such thatφ m (p 2) hasa large prime factor, where φ m (x ) is the m φ th cyclotomicpolynomial and m = 3 or m = 6. An unconditionallypolynomial time algorithm for generating primes of the above formis not yet known. Generating primes of such form is essential forthe GH and the CEILIDH Public Key Systems, since they are keyparameters in these cryptosystems.