A Complete Evaluation of Arithmetic in Real Hyperelliptic Curves
Abstract
Real hyperelliptic curves admit two structures: the Jacobian and the infrastructure. While both structures in real models could be employed for cryptographic purposes, it was not clear which one has better performance in practice. Mireles Morales [46]
described the relationship between these two structures, and made the assertion that when implemented with balanced divisor arithmetic, the Jacobian generically yields more efficient arithmetic than the infrastructure for cryptographic applications. However, he did not support his claim via a mathematical proof or an implementation.
In this thesis, we describe that exactly how the infrastructure and the Jacobian are related through an accurate and detailed mathematical and computational analysis. We suggest an alternative distance map for the infrastructure in order to improve the efficiency of this structure. Our mathematical investigation shows that the infrastructure with the new distance and the Jacobian have identical performance in practice for cryptographic sized curves. We prove this results mathematically and verify their correctness computationally.
Description
Keywords
Education--Mathematics
Citation
Rezai Rad, M. (2016). A Complete Evaluation of Arithmetic in Real Hyperelliptic Curves (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24673