On implementation of Stickel's key exchange protocol over max-min and max-T semirings

Given that the tropical Stickel protocol and its variants are all vulnerable to the generalized Kotov–Ushakov attack, we suggest employing the max-min semiring and, more generally, max- semiring where the multiplication is based on a -norm, as a framework to implement the Stickel protocol. While the...

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Published inJournal of mathematical cryptology Vol. 18; no. 1; pp. 644 - 54
Main Authors Alhussaini, Sulaiman, Sergeev, Sergeĭ
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 26.11.2024
Walter de Gruyter GmbH
Subjects
08A72
15A80
94A60
cryptographic attack
fuzzy algebra
fuzzy relation equations
public key cryptography
Rings (mathematics)
Stickel protocol
Online AccessGet full text
ISSN1862-2984
1862-2976
1862-2984
DOI10.1515/jmc-2024-0014

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Abstract Given that the tropical Stickel protocol and its variants are all vulnerable to the generalized Kotov–Ushakov attack, we suggest employing the max-min semiring and, more generally, max- semiring where the multiplication is based on a -norm, as a framework to implement the Stickel protocol. While the Stickel protocol over max-min semiring or max- semiring remains susceptible to a form of Kotov–Ushakov attack, we demonstrate that it exhibits significantly increased resistance against this attack when compared to the tropical (max-plus) implementation.
AbstractList Given that the tropical Stickel protocol and its variants are all vulnerable to the generalized Kotov–Ushakov attack, we suggest employing the max-min semiring and, more generally, max-TT semiring where the multiplication is based on a TT-norm, as a framework to implement the Stickel protocol. While the Stickel protocol over max-min semiring or max-TT semiring remains susceptible to a form of Kotov–Ushakov attack, we demonstrate that it exhibits significantly increased resistance against this attack when compared to the tropical (max-plus) implementation.
Given that the tropical Stickel protocol and its variants are all vulnerable to the generalized Kotov–Ushakov attack, we suggest employing the max-min semiring and, more generally, max- semiring where the multiplication is based on a -norm, as a framework to implement the Stickel protocol. While the Stickel protocol over max-min semiring or max- semiring remains susceptible to a form of Kotov–Ushakov attack, we demonstrate that it exhibits significantly increased resistance against this attack when compared to the tropical (max-plus) implementation.
Given that the tropical Stickel protocol and its variants are all vulnerable to the generalized Kotov–Ushakov attack, we suggest employing the max-min semiring and, more generally, max- [Image omitted] semiring where the multiplication is based on a [Image omitted] -norm, as a framework to implement the Stickel protocol. While the Stickel protocol over max-min semiring or max- [Image omitted] semiring remains susceptible to a form of Kotov–Ushakov attack, we demonstrate that it exhibits significantly increased resistance against this attack when compared to the tropical (max-plus) implementation.
Given that the tropical Stickel protocol and its variants are all vulnerable to the generalized Kotov–Ushakov attack, we suggest employing the max-min semiring and, more generally, max- T T semiring where the multiplication is based on a T T -norm, as a framework to implement the Stickel protocol. While the Stickel protocol over max-min semiring or max- T T semiring remains susceptible to a form of Kotov–Ushakov attack, we demonstrate that it exhibits significantly increased resistance against this attack when compared to the tropical (max-plus) implementation.
Author Alhussaini, Sulaiman
Sergeev, Sergeĭ
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10.1080/00927872.2021.1975125
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10.1080/00927872.2019.1581213
10.1016/j.fss.2014.11.008
10.1080/00927872.2013.766827
10.21136/AM.2020.0325-19
10.1109/TIT.1976.1055638
10.1016/S0167-6377(02)00159-1
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2024112615512245232_j_jmc-2024-0014_ref_009
2024112615512245232_j_jmc-2024-0014_ref_004
2024112615512245232_j_jmc-2024-0014_ref_015
2024112615512245232_j_jmc-2024-0014_ref_005
2024112615512245232_j_jmc-2024-0014_ref_016
2024112615512245232_j_jmc-2024-0014_ref_006
2024112615512245232_j_jmc-2024-0014_ref_017
2024112615512245232_j_jmc-2024-0014_ref_007
2024112615512245232_j_jmc-2024-0014_ref_018
2024112615512245232_j_jmc-2024-0014_ref_011
2024112615512245232_j_jmc-2024-0014_ref_022
2024112615512245232_j_jmc-2024-0014_ref_001
2024112615512245232_j_jmc-2024-0014_ref_012
2024112615512245232_j_jmc-2024-0014_ref_023
2024112615512245232_j_jmc-2024-0014_ref_002
2024112615512245232_j_jmc-2024-0014_ref_013
2024112615512245232_j_jmc-2024-0014_ref_003
2024112615512245232_j_jmc-2024-0014_ref_014
2024112615512245232_j_jmc-2024-0014_ref_020
2024112615512245232_j_jmc-2024-0014_ref_010
2024112615512245232_j_jmc-2024-0014_ref_021
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  doi: 10.1109/ICITA.2005.33
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  doi: 10.1142/5683
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  doi: 10.1016/S0012-365X(02)00754-9
– ident: 2024112615512245232_j_jmc-2024-0014_ref_010
  doi: 10.1090/conm/616/12301
– ident: 2024112615512245232_j_jmc-2024-0014_ref_017
  doi: 10.3934/math.2023885
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  doi: 10.1080/23799927.2020.1862303
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  doi: 10.3390/app12157401
– ident: 2024112615512245232_j_jmc-2024-0014_ref_009
  doi: 10.1515/jmc-2019-0061
– ident: 2024112615512245232_j_jmc-2024-0014_ref_018
– ident: 2024112615512245232_j_jmc-2024-0014_ref_004
  doi: 10.1515/jmc-2016-0064
– ident: 2024112615512245232_j_jmc-2024-0014_ref_013
  doi: 10.1016/0165-0114(84)90026-5
– ident: 2024112615512245232_j_jmc-2024-0014_ref_008
  doi: 10.1080/00927872.2021.1975125
– ident: 2024112615512245232_j_jmc-2024-0014_ref_014
– ident: 2024112615512245232_j_jmc-2024-0014_ref_019
  doi: 10.1016/S0165-0114(01)00108-7
– ident: 2024112615512245232_j_jmc-2024-0014_ref_006
  doi: 10.1080/00927872.2019.1581213
– ident: 2024112615512245232_j_jmc-2024-0014_ref_011
  doi: 10.1016/j.fss.2014.11.008
– ident: 2024112615512245232_j_jmc-2024-0014_ref_012
– ident: 2024112615512245232_j_jmc-2024-0014_ref_003
  doi: 10.1080/00927872.2013.766827
– ident: 2024112615512245232_j_jmc-2024-0014_ref_005
  doi: 10.21136/AM.2020.0325-19
– ident: 2024112615512245232_j_jmc-2024-0014_ref_020
– ident: 2024112615512245232_j_jmc-2024-0014_ref_001
  doi: 10.1109/TIT.1976.1055638
– ident: 2024112615512245232_j_jmc-2024-0014_ref_022
  doi: 10.1016/S0167-6377(02)00159-1
– ident: 2024112615512245232_j_jmc-2024-0014_ref_023
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SubjectTerms 08A72
15A80
94A60
cryptographic attack
fuzzy algebra
fuzzy relation equations
public key cryptography
Rings (mathematics)
Stickel protocol
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Title On implementation of Stickel's key exchange protocol over max-min and max-T semirings
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