Public Key Encryption from High-Corruption Constraint Satisfaction Problems

2026-04-12

AI Summary

This work proposes the first public-key encryption scheme achieving quasi-exponential security for constraint satisfaction problems (CSPs) under extremely high noise regimes—specifically, when the corruption rate approaches one. The construction relies on two hardness assumptions: a newly introduced LARP-CSP problem and the high-noise kXOR problem. A key innovation lies in embedding cryptographic trapdoors via label-extended factor graphs. The main contributions include the first demonstration of public-key encryption based on highly corrupted CSPs that surpasses quasipolynomial security, the design of an error-correcting code featuring both low-density generator matrices and efficient decoding, and the establishment of strong security guarantees through multiple lower-bound results that rule out known attack strategies.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

We give a public key encryption scheme with plausible quasi-exponential security based on the conjectured intractability of two constraint satisfaction problems (CSPs), both of which are instantiated with a corruption rate of $1 - o(1)$. First, we conjecture the hardness of a new large alphabet random predicate CSP (LARP-CSP) defined over an arbitrary but strongly expanding factor graph, where the vast majority of predicate outputs are replaced with random outputs. Second, we conjecture the hardness of the standard $k$XOR problem defined over a random factor graph, again where the vast majority of parity computations are replaced with random bits. In support of our hardness conjecture for LARP-CSPs, we give a variety of lower bounds, ruling out many natural attacks including all known attacks that exploit non-random factor graphs. Our public key encryption scheme is the first to leverage high corruption CSPs while simultaneously achieving a plausible security level far above quasi-polynomial. At the heart of our work is a new method for planting cryptographic trapdoors based on the label extended factor graph for a CSP. Along the way to achieving our result, we give the first uniform construction of an error-correcting code that has an expanding, low density generator matrix while simultaneously allowing for efficient decoding from a $1 - o(1)$ fraction of corruptions.

Problem

• public key encryption
• constraint satisfaction problems
• high corruption
• quasi-exponential security
• LARP-CSP

Innovation

• high-corruption CSP
• public key encryption
• quasi-exponential security
• trapdoor planting
• error-correcting code