In this paper, we present for the first time efficient explicit formulas for arithmetic in the degree 0 divisor class group of a real hyperelliptic curve. Hereby, we consider real hyperelliptic curves of genus 2 given in affine coordinates for which the underlying finite field has characteristic > 3. These formulas are much faster than the optimized generic algorithms for real hyperelliptic curves and the cryptographic protocols in the real setting perform almost as well as those in the imaginary case. We provide the idea for the improvements and the correctness together with a comprehensive analysis of the number of field operations. Finally, we perform a direct comparison of cryptographic protocols using explicit formulas for real hyperelliptic curves with the corresponding protocols presented in the imaginary model. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Erickson, S., Jacobson, M. J., Shang, N., Shen, S., & Stein, A. (2007). Explicit formulas for real hyperelliptic curves of genus 2 in affine representation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4547 LNCS, pp. 202–218). Springer Verlag. https://doi.org/10.1007/978-3-540-73074-3_16
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