Welcome to the resource topic for 2025/1191
Title:
A Polynomial Public-Key Cryptosystem Based on Jacobian-Preserving Composition
Authors: Saimon Ahmed
Abstract:We propose a public-key cryptosystem based on Jacobian-preserving polynomial compositions, utilizing algebraically invertible polynomial maps with hard-to-invert composition. The construction utilizes polynomial maps over \mathbb{Z}_p, where p is a prime number, with Jacobian determinant equal to 1 to ensure invertibility. The public key function H : \mathbb{Z}_p^n \to \mathbb{Z}_p^n is defined as the composition of invertible polynomial maps f_1, f_2, \dots, f_k, each with Jacobian determinant 1, while the private key consists of the individual components used in the composition. Although inverting the composition is possible, inverting without the knowledge of the factors is computationally infeasible. This system incorporates both triangular and affine polynomial maps. We discuss the construction, provide formal correctness proofs, analyze hardness assumptions, and present a Python-based prototype with benchmark results.
ePrint: https://eprint.iacr.org/2025/1191
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .