On symbolic computations and Post Quantum Cryptography with Lie Geometries.

Vasyl Ustimenko

Paper 2025/1195

On symbolic computations and Post Quantum Cryptography with Lie Geometries.

Vasyl Ustimenko

, Royal Holloway University of London

Abstract

Assume that the global density of multivariate map over the commutative ring is the total number of its coefficients. In the case of finite commutative ring K with the multiplicative group K* containing more than 2 elements we suggest multivariate public keys in n variables with the public rule of global density O(n) and degree O(1). Another public keys use public rule of global density O(n) and degree O(n) together with the space of plaintexts (K*)^n and the space of ciphertext K^n . We consider examples of protocols of Noncommutative Cryptography implemented on the platform of endomorphisms of which allow the con-version of mentioned above multivariate public keys into protocol based cryptosystems of El Gamal type. The cryptosystems and protocols are designed in terms of analogue of geometries of Chevalley groups over commutative rings and their temporal versions.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Symbolic Computation Lie geometries Noncommutative Cryptography Multivariate public keys
Contact author(s): Vasyl Ustymenko @ rhul ac uk
History: 2025-06-30: approved; 2025-06-26: received; See all versions
Short URL: https://ia.cr/2025/1195
License: CC BY

BibTeX

@misc{cryptoeprint:2025/1195,
      author = {Vasyl Ustimenko},
      title = {On symbolic computations and Post Quantum Cryptography with Lie Geometries.},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1195},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1195}
}