A Contribution to the Discrete Logarithm Problem

• Autorzy: Paszkiewicz A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider a common, fundamental problem of all cryptographic schemes based on the discrete logarithm modulo a prime. This is the choice a base of the modular exponent function or other words a generator of a prime order multiplicative group. We construct a class of primes for which its least generators can be extremely large.

Słowa kluczowe

EN

discrete logarithm problem; multiplicative group modulo a prime; least quadratic non-residue; least primitive root

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: Electronics and Telecommunications Quarterly
• Rocznik: 2009
• Tom: Vol. 55, No 3
• Strony: 493--499
• Opis fizyczny: Bibliogr. 5 poz., wykr.

Twórcy

autor

Paszkiewicz A.

• Warsaw University of Technology,

Bibliografia

• 1. P. D. T. A. Elliott, L. Murata: On the average value of the least primitive root modulo p, J. London Math. Soc. 56, pp. 435-454, 1997
• 2. S. W. Graham, C. J. Ringrose. Lower bounds for least quadratic non-residues, Analytic Number Theory, Proceedings in Honor of Paul T. Bateman, Progress in Mathematics 85, pp. 269-309, Birkhauser, Boston 1990
• 3. K. Ireland, M. Rosen, A Classical Introduction to modern Number Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1982, Graduate Texts in Mathematics, 87
• 4. A. Menezes et all, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997
• 5. A. Paszkiewicz: On the least prime primitive root modulo a prime, Math. Comp. v. 71, no. 239, pp. 1307-1321, 2002