Algorithm for Generating Primes p and q Such that q Divides p₄ ± p₃ + p₂ ± p + 1

Issue title: Cryptology in Progress: 10th Central European Conference on Cryptology, Będlewo Poland, 2010

Article type: Research Article

Authors: Grześkowiak, Maciej

Affiliations: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland. [email protected]

Note: [] Address for correspondence: Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Umultowska 87, 61-614 Poznań, Poland Partially supported by Ministry of Science and Higher Education, grant N N201 1482 33, 2007–2010

Abstract: In the paper we propose an algorithm for generating large primes p and q such that q divides p4 + p3 + p2 + p + 1 or p4 − p3 + p2 − p + 1, and p, q are key parameters for Giuliani-Gong's Public Key System. We analyze the computational complexity of considered methods.

Keywords: The Giuliani-Gong Public Key System, primes of special form

DOI: 10.3233/FI-2012-629

Journal: Fundamenta Informaticae, vol. 114, no. 3-4, pp. 287-299, 2012