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Lecture notes in computer science

Error Correction and Ciphertext Quantization in Lattice Cryptography

Daniele Micciancio, Mark Schultz-Wu

Published Jan 1, 2023• 7 citations
Publisher
DOI
10.1007/978-3-031-38554-4_21

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The advent of quantum computing poses a significant threat to traditional cryptographic algorithms, including RSA, Diffie-Hellman, and Elliptic Curve Cryptography, due to the capabilities of quantum algorithms like Shor’s algorithm. Post-quantum cryptography (PQC) has emerged to address these challenges, with lattice-based cryptography (LBC) being a prominent candidate. LBC, underpinned by hard mathematical problems like Learning with Errors (LWE) and Ring-LWE (RLWE), offers robust security against quantum and classical adversaries. In parallel, Ciphertext-Policy Attribute-Based Encryption (CPABE) has become a critical tool for enabling fine-grained access control in data-sharing scenarios, such as secure cloud storage and IoT. While existing CP-ABE implementations rely on bilinear pairings vulnerable to quantum attacks, lattice-based CPABE schemes provide a quantum-resistant alternative. Despite their potential, these schemes face challenges in computational efficiency, collusion resistance, and implementation correctness. Our contributions include a detailed mathematical breakdown of one of the state-of-the-art (SOTA) lattice-based CP-ABE schemes and a novel correctness proof for the same scheme.
Abstract The advancement of quantum attacks has posed a significant threat to blockchain cryptosystems. Furthermore, the finite lifecycles of ciphertext and keys may result in data leakage risks for long-term storage due to potential breaches in ciphertext security, necessitating ciphertext updates. Ensuring the long-term security of cryptographic algorithms on blockchains against quantum attacks has emerged as a critical concern in blockchain research. A blockchain oracle serves as a mechanism for data communication. The Module-Learning with Errors (MLWE) problem is a significant issue in lattice-based cryptography, providing security against quantum attacks. To resist the threat of quantum attacks on encrypted data and ensure the long-term security, this study proposed an updatable encryption (UE) scheme for blockchain oracles based on post-quantum cryptography. First, this study developed a UE scheme based on the blockchain oracle architecture, enabling the oracle to update encrypted data via update tokens, ensuring the data's long-term security. Additionally, a UE algorithm based on the MLWE problem was introduced to enhance its resistance to quantum attacks. Finally, an error-correcting mechanism tailored for the UE algorithm was developed to validate transmitted data, correct errors, and improve the scheme's robustness. The experimental results demonstrate that the proposed scheme not only provides quantum-resistant security but also enables ciphertext updates through update tokens. Compared to existing schemes, it has more advantages in protecting data security.
Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries of this noise-reliant model across four interconnected domains: computational complexity, information-theoretic thermodynamics, quantum error correction, and quantum learning theory. Starting from the algorithmic foundation, our analysis notes that these frameworks rely on provisional complexity-theoretic assumptions that remain vulnerable to future quantum algorithmic advancements. Furthermore, by translating this cryptographic mechanism into physical thermodynamics, we illustrate that intentionally injected discrete Gaussian noise does not equate to the permanent erasure of information. Because the structural integrity of the cryptographic secret remains preserved within the ciphertext, advanced quantum error correction protocols and quantum learning models can efficiently extract the underlying mathematical kernel. Ultimately, we suggest that while lattice-based cryptography provides a robust transitional alternative, definitively classifying these frameworks as unconditionally post-quantum represents a premature classification relying on transient physical bottlenecks rather than impenetrable theoretical boundaries.