Paper 2024/1714

Theoretical Approaches to Solving the Shortest Vector Problem in NP-Hard Lattice-Based Cryptography with Post-SUSY Theories of Quantum Gravity in Polynomial Time

Abstract

The Shortest Vector Problem (SVP) is a cornerstone of lattice-based cryptography, underpinning the security of numerous cryptographic schemes like NTRU. Given its NP-hardness, efficient solutions to SVP have profound implications for both cryptography and computational complexity theory. This paper presents an innovative framework that integrates concepts from quantum gravity, noncommutative geometry, spectral theory, and post-SUSY particle physics to address SVP. By mapping high-dimensional lattice points to spin foam networks and by means of Hamiltonian engineering, it is theoretically possible to devise new algorithms that leverage the interactions topologically protected Majorana fermion particles have with the gravitational field through the spectral action principle to loop through these spinfoam networks where SVP vectors could then be encoded onto the spectrum of the corresponding Dirac operators within the system. We establish a novel approach that leverages post-SUSY physics and theories of quantum gravity to achieve algorithmic speedups beyond those expected by conventional quantum computers. This interdisciplinary methodology not only proposes potential polynomial-time algorithms for SVP but also bridges gaps between theoretical physics and cryptographic applications, providing further insights into the Riemann Hypothesis (RH) and the Hilbert-Polya Conjecture.

Note: Revision added nuance between NP-hard, NP-complete, and NP, with additional citations.