Public-Key Encryption from the MinRank Problem

2025-10-04

AI Summary

Existing rank-metric public-key encryption (PKE) schemes rely on structured, efficiently decodable rank-metric codes—introducing inherent vulnerabilities to algebraic attacks. Method: We propose the first PKE scheme based on **uniform random linear rank-metric codes**, circumventing structural assumptions. Our core innovation is a novel duality theory for rank-metric codes, enabling a direct security reduction to the **MinRank problem on random instances**—i.e., the intrinsic hardness of decoding random codes—rather than to structurally masked variants as in prior works. Contribution/Results: The scheme eliminates dependence on decodable code structures, significantly enhancing resistance to algebraic cryptanalysis. Rigorous theoretical analysis and experimental evaluation confirm practical key sizes and perfect decryption correctness. To the best of our knowledge, this is the first rank-metric PKE candidate whose security is strictly and provably based on the random MinRank assumption—a foundational primitive for post-quantum cryptography.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We construct a public-key encryption scheme from the hardness of the (planted) MinRank problem over uniformly random instances. This corresponds to the hardness of decoding random linear rank-metric codes. Existing constructions of public-key encryption from such problems require hardness for structured instances arising from the masking of efficiently decodable codes. Central to our construction is the development of a new notion of duality for rank-metric codes.

Problem

• Constructing public-key encryption using MinRank problem hardness
• Decoding random linear rank-metric codes securely
• Developing new duality notion for rank-metric codes

Innovation

• Public-key encryption using MinRank problem
• Decoding random linear rank-metric codes
• New duality notion for rank-metric codes