Generating elements of orders dividing p6 ± p5 + p4 ± p3 + p2 + p ± 1

• Autorzy: Grześkowiak M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we propose an algorithm for computing large primes p and q such that q divides p6 + p5 + p4 + p3 + p2 + p + 1 or p6 - p5 + p4 - p3 + p2 - p + 1. Such primes are the key parameters for the cryptosystem based on the 7th order characteristic sequences.

Słowa kluczowe

EN

cryptosystem; prime numbers; algorithm

• Wydawca: Wydawnictwo UMCS
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica
• Rocznik: 2011
• Tom: Vol. 11, no. 2
• Strony: 113--125
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Grześkowiak M.

• Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Umultowska 87, 61-614 Poznań, Poland

Bibliografia

• [1] Lenstra A. K., Verhuel E. R., The XTR Public Key System, Proceedings of Crypto 2000, LNCS 1880, Springer-Verlag (2000): 1.
• [2] Gong G., Harn L., Public-Key Cryptosystems Based on Cubic Finite Field Extension, IEEE IT, 45(7) (1999): 2601.
• [3] Gong G., Harn L., A New Approach on Public{key Distribution, ChinaCRYPT (1998): 50.
• [4] Giuliani K., Gong G., Analogues to the Gong{Harn and XTR Cryptosystem, Combinatorics and Optimization Research Report CORR 2003{34, University of Waterloo (2003).
• [5] Giuliani K., Gong G., New LFSR-Based Cryptosystems and the Trace Discrete Log Problem (Trace-DLP), In: Sequence and Their Applications, SETA 2004. LNCS 3486, Springer-Verlag (2005): 298.
• [6] Cox D. A., Primes of the forms x2 + ny2, Wiley, New York (1989).