Paper 2024/697

LINE: Cryptosystem based on linear equations for logarithmic signatures

Gennady Khalimov, Kharkiv National University of Radioelectronics
Yevgen Kotukh, Yevhenii Bereznyak Military Academy
Maksym Kolisnyk, Kharkiv National University of Radioelectronics
Svitlana Khalimova, Kharkiv National University of Radioelectronics
Oleksandr Sievierinov, Kharkiv National University of Radioelectronics
Abstract

The discourse herein pertains to a directional encryption cryptosystem predicated upon logarithmic signatures interconnected via a system of linear equations (we call it LINE). A logarithmic signature serves as a foundational cryptographic primitive within the algorithm, characterized by distinct cryptographic attributes including nonlinearity, noncommutativity, unidirectionality, and factorizability by key. The confidentiality of the cryptosystem is contingent upon the presence of an incomplete system of equations and the substantial ambiguity inherent in the matrix transformations integral to the algorithm. Classical cryptanalysis endeavors are constrained by the potency of the secret matrix transformation and the indeterminacy surrounding solutions to the system of linear equations featuring logarithmic signatures. Such cryptanalysis methodologies, being exhaustive in nature, invariably exhibit exponential complexity. The absence of inherent group computations within the algorithm, and by extension, the inability to exploit group properties associated with the periodicity of group elements, serves to mitigate quantum cryptanalysis to Grover's search algorithm. LINE is predicated upon an incomplete system of linear equations embodies the security levels ranging from 1 to 5, as stipulated by the NIST, and thus presents a promising candidate for the construction of post-quantum cryptosystems.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint.
Keywords
LINEPost-quantum cryptosystemLogarithmic signatureDirectional encryption.
Contact author(s)
hennadii khalimov @ nure ua
yevgenkotukh @ gmail com
yevgenkotukh @ gmail com
yevgenkotukh @ gmail com
yevgenkotukh @ gmail com
History
2024-05-10: approved
2024-05-06: received
See all versions
Short URL
https://ia.cr/2024/697
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/697,
      author = {Gennady Khalimov and Yevgen Kotukh and Maksym Kolisnyk and Svitlana Khalimova and Oleksandr Sievierinov},
      title = {{LINE}: Cryptosystem based on linear equations for logarithmic signatures},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/697},
      year = {2024},
      url = {https://eprint.iacr.org/2024/697}
}
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