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May  2007, 1(2): 197-221. doi: 10.3934/amc.2007.1.197

Cryptographic protocols on real hyperelliptic curves

M. J. Jacobson 1, , R. Scheidler 2, and  A. Stein 3,

1. 

Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada
2. 

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada
3. 

Department of Mathematics, University of Wyoming, 1000 E. University Avenue, Laramie, WY 82071-3036, United States

Received  September 2006 Revised  May 2007 Published  May 2007

We present public-key cryptographic protocols for key exchange, digital signatures, and encryption whose security is based on the presumed intractability of solving the principal ideal problem, or equivalently, the distance problem, in the real model of a hyperelliptic curve. Our protocols represent a significant improvement over existing protocols using real hyperelliptic curves. Theoretical analysis and numerical experiments indicate that they are comparable to the imaginary model in terms of efficiency, and hold much more promise for practical applications than previously believed.
Keywords: infrastructure and distance, reduced divisor, Discrete logarithm based cryptography, efficient implementation., real hyperelliptic curve.
Mathematics Subject Classification: Primary: 94A60, 14H45; Secondary: 14Q0.
Citation: M. J. Jacobson, R. Scheidler, A. Stein. Cryptographic protocols on real hyperelliptic curves. Advances in Mathematics of Communications, 2007, 1 (2) : 197-221. doi: 10.3934/amc.2007.1.197
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