Modifying the tropical version of Stickel's key exchange protocol

Any Muanalifah; Sergey Sergeev

doi:10.21136/AM.2020.0325-19

Modifying the tropical version of Stickel's key exchange protocol

Any Muanalifah, Sergey Sergeev

Mathematics

Research output: Contribution to journal › Article › peer-review

252 Downloads (Pure)

Abstract

A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the application of that generalized attack to all our new protocols.

Original language	English
Pages (from-to)	727-753
Number of pages	27
Journal	Applications of Mathematics
Volume	65
Issue number	6
Early online date	27 Oct 2020
DOIs	https://doi.org/10.21136/AM.2020.0325-19
Publication status	Published - 1 Dec 2020

Keywords

Stickel's protocol
commuting matrices
cryptography
tropical algebra

Access to Document

10.21136/AM.2020.0325-19

MuanalifahA2020Modifying
The original publication is available at www.dml.cz
Accepted author manuscript, 541 KBLicence: None: All rights reserved

Tropical Optimisation
Sergeev, S.
Engineering & Physical Science Research Council
1/04/17 → 31/08/19
Project: Research Councils

Cite this

@article{00dd9763297e4f10b415c4929d6c4bd4,

title = "Modifying the tropical version of Stickel's key exchange protocol",

abstract = "A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the application of that generalized attack to all our new protocols.",

keywords = "Stickel's protocol, commuting matrices, cryptography, tropical algebra",

author = "Any Muanalifah and Sergey Sergeev",

year = "2020",

month = dec,

day = "1",

doi = "10.21136/AM.2020.0325-19",

language = "English",

volume = "65",

pages = "727--753",

journal = "Applications of Mathematics",

issn = "0862-7940",

publisher = "Akademie v{\v e}d {\v C}esk{\'e} republiky, Matematick{\'y} {\'u}stav",

number = "6",

}

TY - JOUR

T1 - Modifying the tropical version of Stickel's key exchange protocol

AU - Muanalifah, Any

AU - Sergeev, Sergey

PY - 2020/12/1

Y1 - 2020/12/1

N2 - A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the application of that generalized attack to all our new protocols.

AB - A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the application of that generalized attack to all our new protocols.

KW - Stickel's protocol

KW - commuting matrices

KW - cryptography

KW - tropical algebra

UR - http://am.math.cas.cz/

U2 - 10.21136/AM.2020.0325-19

DO - 10.21136/AM.2020.0325-19

M3 - Article

SN - 0862-7940

VL - 65

SP - 727

EP - 753

JO - Applications of Mathematics

JF - Applications of Mathematics

IS - 6

ER -

Modifying the tropical version of Stickel's key exchange protocol

Abstract

Keywords

Access to Document

Fingerprint

Projects

Tropical Optimisation

Cite this