Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 39 min ago
Peer-reviewedCC BY 4.0Mathematics

Structural Cryptanalysis of a Class-2 Nilpotent Lie Algebra Signature Candidate: Linearization and Equivalent-Secret Forgery

  • Aybeyan Selim1
  • Omer Aydin2
  • Muzafer Saračević3
  • Komlen Lalović4
  • Arsim Susuri5
5 affiliations
  1. 1Faculty of Engineering and Architecture, International Vision University, Major Cede Filipovski, 1230 Gostivar, North Macedonia
  2. 2Electrical and Electronics Engineering, Faculty of Engineering and Natural Sciences, Manisa Celal Bayar University, 45140 Manisa, Türkiye
  3. 3Department of Economics and Computer Sciences, University of Novi Pazar, Dimitrija Tucovica 65, 36300 Novi Pazar, Serbia
  4. 4Faculty of Information Technologies and Engineering, University of Nikola Tesla, 1100 Belgrade, Serbia
  5. 5Faculty of Computer Science, University “Ukshin Hoti” Prizren, Shkronjat, 20000 Prizren, Kosovo
Open at sourceDOICite

Abstract

This study presents a structural cryptanalysis of a Fiat–Shamir-type digital-signature candidate based on class-2 nilpotent Lie algebras over finite fields. We show that the public transformation is linear in the signing secret and that public-key inversion reduces to a consistent linear system over the underlying finite field, solvable in polynomial time by Gaussian elimination. Because the associated linear map has a non-trivial kernel, the public key determines an affine family of equivalent signing secrets rather than a unique private key. Any compatible representative can therefore be used to generate a valid signature for a fresh message without access to a signing oracle, yielding a polynomial-time no-message forgery and failure of EUF-CMA security. The baseline evaluation considered n=16, 32, 64 and 128, using ten independently generated Lie algebra instances per dimension and ten cryptographic trials per instance. In the 400 baseline trials, none of the recovered compatible secrets coincided with the corresponding originally sampled private key, yet every recovered representative was sufficient to generate an accepted forgery, yielding a 100% experimental forgery rate. Additional sensitivity experiments on field size, central fraction, and bracket density showed that these parameters affect practical attack cost and rank-nullity structure but do not remove the vulnerability. The results demonstrate that the examined class-2 transformation is unsuitable as a hardness basis for a secure digital-signature construction or a meaningful post-quantum security claim.

Related

  1. Equivalent linearization modeling and experimental validation of natural frequency and vibration isolation performance in metal braided hoses
    Dacheng Huang, Yue Liu, Dongqin Li +1
    PLOS OnePeer-reviewedCC BY 4.0Full textMaterials & polymersAlgebra & number theoryPLOSPMC
  2. Cryptanalysis of a Class of Ideal Secret Sharing Schemes Based on the CRT for Polynomial Rings
    Jian Ding, Zhiyuan Guo, Hongju Li +1
    arXivPreprintCC BY 4.0Full textGeneral mathematicsarXiv
  3. Cryptanalysis of Image Cryptosystem via Finite-Time Projective Synchronization in Fractional-Order Inertial Memristive Neural Networks
    Yiting Lin, Xiyuan Cheng, Yaokang Li +2
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  4. Endogenies and linearization in the non-virtually connected case
    Moreno Invitti
    HALPreprintCC BY 4.0Full textAlgebra & number theoryLogic & foundationsHAL
  5. Bi-parameter local linearization for the stochastic wave equation with rough noise
    Ruinan Li, Ran Wang
    arXivPreprintCC BY 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@article{selim2026structural,
  title = {{Structural Cryptanalysis of a Class-2 Nilpotent Lie Algebra Signature Candidate: Linearization and Equivalent-Secret Forgery}},
  author = {Aybeyan Selim and Omer Aydin and Muzafer Saračević and Komlen Lalović and Arsim Susuri},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14193617},
  url = {https://www.mdpi.com/2227-7390/14/19/3617},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Structural Cryptanalysis of a Class-2 Nilpotent Lie Algebra Signature Candidate: Linearization and Equivalent-Secret Forgery
AU  - Aybeyan Selim
AU  - Omer Aydin
AU  - Muzafer Saračević
AU  - Komlen Lalović
AU  - Arsim Susuri
PY  - 2026
DA  - 2026/10/06
JO  - Mathematics
DO  - 10.3390/math14193617
UR  - https://www.mdpi.com/2227-7390/14/19/3617
AB  - This study presents a structural cryptanalysis of a Fiat–Shamir-type digital-signature candidate based on class-2 nilpotent Lie algebras over finite fields. We show that the public transformation is linear in the signing secret and that public-key inversion reduces to a consistent linear system over the underlying finite field, solvable in polynomial time by Gaussian elimination. Because the associated linear map has a non-trivial kernel, the public key determines an affine family of equivalent signing secrets rather than a unique private key. Any compatible representative can therefore be used to generate a valid signature for a fresh message without access to a signing oracle, yielding a polynomial-time no-message forgery and failure of EUF-CMA security. The baseline evaluation considered n=16, 32, 64 and 128, using ten independently generated Lie algebra instances per dimension and ten cryptographic trials per instance. In the 400 baseline trials, none of the recovered compatible secrets coincided with the corresponding originally sampled private key, yet every recovered representative was sufficient to generate an accepted forgery, yielding a 100% experimental forgery rate. Additional sensitivity experiments on field size, central fraction, and bracket density showed that these parameters affect practical attack cost and rank-nullity structure but do not remove the vulnerability. The results demonstrate that the examined class-2 transformation is unsuitable as a hardness basis for a secure digital-signature construction or a meaningful post-quantum security claim.
SN  - 2227-7390
ER  -