Tropical cryptography III: digital signatures
Jiale Chen, Dima Grigoriev, Vladimir Shpilrain
TL;DR
The paper proposes an efficient digital signature framework based on the min-plus tropical semiring, using one-variable tropical polynomials to construct a public key via $M=X\otimes Y$ and a hash-to-polynomial mapping for signing. Security hinges on the NP-hardness of factoring tropical polynomials, while the authors discuss known forgery attacks and present countermeasures, including an alternative scheme that adds tropical addition to resist division-based attacks. Concrete parameter choices and irreducibility considerations are provided to promote secure key-generation, along with explicit performance and size metrics showing relatively compact keys and signatures on modest hardware. The work demonstrates the viability of tropical cryptography for signatures, analyzes potential vulnerabilities, and offers practical guidance for implementation and future defenses against attacks such as Brown–Monico.
Abstract
We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard.