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Cryptography from the tropical Hessian pencil

Cryptography from the tropical Hessian pencil AbstractRecent work by Grigoriev and Shpilrain [8] suggests looking at the tropical semiring for cryptographic schemes. In this contribution we explore the tropical analogue of the Hessian pencil of plane cubic curves as a source of group-based cryptography. Using elementary tropical geometry on the tropical Hessian curves, we derive the addition and doubling formulas induced from their Jacobian and investigate the discrete logarithm problem in this group. We show that the DLP is solvable when restricted to integral points on the tropical Hesse curve, and hence inadequate for cryptographic applications. Consideration of point duplication, however, provides instances of solvable chaotic maps producing random sequences and thus a source of fast keyed hash functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Cryptography from the tropical Hessian pencil

Groups Complexity Cryptology , Volume 9 (1): 11 – May 1, 2017

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Publisher
de Gruyter
Copyright
© 2017 by De Gruyter
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2017-0002
Publisher site
See Article on Publisher Site

Abstract

AbstractRecent work by Grigoriev and Shpilrain [8] suggests looking at the tropical semiring for cryptographic schemes. In this contribution we explore the tropical analogue of the Hessian pencil of plane cubic curves as a source of group-based cryptography. Using elementary tropical geometry on the tropical Hessian curves, we derive the addition and doubling formulas induced from their Jacobian and investigate the discrete logarithm problem in this group. We show that the DLP is solvable when restricted to integral points on the tropical Hesse curve, and hence inadequate for cryptographic applications. Consideration of point duplication, however, provides instances of solvable chaotic maps producing random sequences and thus a source of fast keyed hash functions.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2017

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