Paper 2021/898

On Extremal Expanding Algebraic Graphs and post-quantum secure delivery of passwords, encryption maps and tools for multivariate digital signatures.

Vasyl Ustimenko

Abstract

Expanding graphs are known due to their remarkable applications to Computer Science. We are looking for their applications to Post Quantum Cryptography. One of them is postquantum analog of Diffie-Hellman protocol in the area of intersection of Noncommutative and Multivariate Cryptographies .This graph based protocol allows correspondents to elaborate collision cubic transformations of affine space Kn defined over finite commutative ring K. Security of this protocol rests on the complexity of decomposition problem of nonlinear polynomial map into given generators. We show that expanding graphs allow to use such output as a ‘’seed’’ for secure construction of infinite sequence of cubic transformation of affine spaces of increasing dimension. Correspondents can use the sequence of maps for extracting passwords for one time pads in alphabet K and other symmetric or asymmetric algorithms. We show that cubic polynomial maps of affine spaces of prescribed dimension can be used for transition of quadratic public keys of Multivariate Cryptography into the shadow of private areas.

Note: None.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Preprint. Minor revision.
Keywords
Extremal Graph TheoryPost Quantum CryptographyMultivariate Cryptographystable subgroups of affine Cremona groupNoncommutative Cryptographykey exchange protocolsrandom and pseudorandom sequencesdigital signatures.
Contact author(s)
vasyl @ hektor umcs lublin pl
History
2021-07-01: received
Short URL
https://ia.cr/2021/898
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/898,
      author = {Vasyl Ustimenko},
      title = {On Extremal Expanding Algebraic Graphs and post-quantum secure delivery of passwords,  encryption maps and tools for multivariate digital signatures.},
      howpublished = {Cryptology ePrint Archive, Paper 2021/898},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/898}},
      url = {https://eprint.iacr.org/2021/898}
}
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