Trapdoor constructions are an active research area in Multivariate Cryptography. The presented work studies trapdoors based on factor decomposition in algebraic structures, with emphasis on polynomial rings over $F_p$. The main contribution is the formulation of a general property: if an algebraic structure admits a hidden factor decomposition then this property can be used as a trapdoor principle. Based on this approach, two constructions are given: one signature scheme and one encryption scheme.
BibTeX
@misc{cryptoeprint:2026/797,
author = {Borja Gomez},
title = {Factorisation-Based Multivariate Schemes: Structural Properties and New Constructions},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/797},
year = {2026},
url = {https://eprint.iacr.org/2026/797}
}
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