Paper 2025/1195 Original: eprint.iacr.org/2025/1195 ↗
On symbolic computations and Post Quantum Cryptography with Lie Geometries.
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.
- History
- 2025-06-26: last updated
- 2025-06-26: published
- Short URL
- https://ia.cr/2025/1195
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}