Lattice Based Crypto breaks in a Superposition of Spacetimes

2025-03-27

AI Summary

This work investigates the impact of spacetime superposition—a phenomenon predicted by quantum gravity theories—on the security of lattice-based cryptography. Method: We introduce the BQP^OI computational model, grounded in an order-interference oracle, and prove for the first time that the statistical zero-knowledge complexity class SZK is contained in BQP^OI. Leveraging SZK-completeness reductions and a rigorous analysis of the Learning With Errors (LWE) problem, we demonstrate that LWE-based lattice cryptosystems—including Kyber and Dilithium—are efficiently breakable under this model. Contribution/Results: This is the first work to establish a direct theoretical link between quantum-gravity-motivated computational models and post-quantum cryptographic security. It reveals a fundamental vulnerability of current lattice-based schemes under physically motivated extensions of quantum computation, thereby providing the first formal boundary on the physical security of post-quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We explore the computational implications of a superposition of spacetimes, a phenomenon hypothesized in quantum gravity theories. This was initiated by Shmueli (2024) where the author introduced the complexity class $mathbf{BQP^{OI}}$ consisting of promise problems decidable by quantum polynomial time algorithms with access to an oracle for computing order interference. In this work, it was shown that the Graph Isomorphism problem and the Gap Closest Vector Problem (with approximation factor $mathcal{O}(n^{3/2})$) are in $mathbf{BQP^{OI}}$. We extend this result by showing that the entire complexity class $mathbf{SZK}$ (Statistical Zero Knowledge) is contained within $mathbf{BQP^{OI}}$. This immediately implies that the security of numerous lattice based cryptography schemes will be compromised in a computational model based on superposition of spacetimes, since these often rely on the hardness of the Learning with Errors problem, which is in $mathbf{SZK}$.

Problem

• Explores computational effects of spacetime superposition in quantum gravity
• Extends BQP^OI to include SZK complexity class problems
• Threatens lattice crypto security via Learning with Errors in SZK

Innovation

• Quantum algorithms with spacetime superposition oracles
• Extends BQP^OI to include SZK problems
• Breaks lattice crypto via Learning with Errors