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- Title
Complete Analysis of Isogeny on Hessian Curve.
- Authors
Rathor, Akash; Kumar, Manoj; Mishra, R. K.; Goswami, Shivender
- Abstract
Isogeny-based cryptography holds significant promise in the realm of post-quantum cryptography, primarily due to its perceived resilience against attacks from quantum computers, based on our current understanding of the underlying mathematical problems. However, it's essential to acknowledge the dynamic nature of post-quantum cryptography, where ongoing research may yield profound insights or lead to the development of novel cryptographic approaches. This study delves into the analysis of Hessian form curves within the framework of isogeny-based cryptography (IBC). We specifically investigate the computational costs associated with deriving Hessian form curves for constructing sections, particularly when employing compression functions. The square-root Velu method is utilized for handling Hessian form curves, and we introduce a novel formula for calculating the curve's coefficient at a specific point on a Hessian curve. Our results indicate that the operational costs of the Hessian form and the Montgomery curve are comparable. Furthermore, we propose the Hessian-Edwards hybrid model, optimizing Hessian-CSIDH and determining the coefficient for the codomain's curve using Edwards curves. According to our findings, various Isogeny-based cryptosystems can be implemented by leveraging Hessian curves.
- Subjects
QUANTUM cryptography; CRYPTOGRAPHY; QUANTUM computers; OPERATING costs; CRYPTOSYSTEMS
- Publication
IAENG International Journal of Computer Science, 2024, Vol 51, Issue 7, p906
- ISSN
1819-656X
- Publication type
Article