A cryptographic application of the Thurston norm

Abstract

We discuss some applications of 3-manifold topology to cryptography. In particular, we propose a public-key and a symmetric-key cryptographic scheme based on the Thurston norm on the first cohomology of hyperbolic manifolds.

Keywords:

• Hyperbolic
• 3-manifold
• Thurston norm
• cryptography
• public key

2010 Mathematics Subject Classification:

• 57M50

Acknowledgments

The authors thank the anonymous referees for their careful reading of the manuscript and for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Ramón Flores is partially supported by FEDER-MINECO (Ministerio de Economia y Competitividad) [grant number MTM2016-76453-C2-1-P]; Delaram Kahrobaei was supported by the ONR (Office of Naval Research) [grant number N000141512164]; Thomas Koberda is partially supported by an Alfred P. Sloan Foundation Research Fellowship and by NSF-Center for Hierarchical Manufacturing, National Science Foundation [grant number DMS-1711488].