IJPAM: Volume 70, No. 4 (2011)

FINDING $N$-TH ROOTS IN NILPOTENT GROUPS
AND APPLICATIONS IN CRYPTOLOGY

Sandra Sze$^1$, Delaram Kahrobaei$^2$, Renald Dambreville$^3$, Makenson Dupas$^4$
$^1$Doctoral Program in Mathematics Department
CUNY Graduate Center
365, Fifth Avenue, New York, NY 10016, USA
$^2$Doctoral Program in Computer Science
CUNY Graduate Center
365, Fifth Avenue, New York, NY 10016, USA
$^{2, 3, 4}$Mathematics Department
New York City College of Technology
300, Jay Street, Brooklyn, NY 11201, USA


Abstract. In this paper we discuss finding $n$-th roots in nilpotent groups and post some open questions. In the literature, the study of finding square root in finite fields has been of interest and because of the complexity of this problem, it has been used in public key cryptography. In this paper, we propose how to find the $n$-th root in nilpotent groups and propose a digital signature based on the semigroup law of $4$-Engel groups.

Received: February 17, 2011

AMS Subject Classification: 20F18, 68P25, 94A60, 11T71

Key Words and Phrases: $n$-th roots, nilpotent groups, digital signature

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 4