Recent work in the design of rate 1 - o(1 ) lattice-based cryptosystems have used two distinct design paradigms, namely replacing the noise-tolerant encoding m↦ (q/ 2 ) m present in many lattice-based cryptosystems with a more efficient encoding, and post-processing traditional lattice-based ciphertexts with a lossy compression algorithm, using a technique very similar to the technique of “vector quantization” within coding theory. We introduce a framework for the design of lattice-based encryption that captures both of these paradigms, and prove information-theoretic rate bounds within this framework. These bounds separate the settings of trivial and non-trivial quantization, and show the impossibility of rate 1 - o(1 ) encryption using both trivial quantization and polynomial modulus. They furthermore put strong limits on the rate of constructions that utilize lattices built by tensoring a lattice of small dimension with Zk, which is ubiquitous in the literature. We additionally introduce a new cryptosystem, that matches the rate of the highest-rate currently known scheme, while encoding messages with a “gadget”, which may be useful for constructions of Fully Homomorphic Encryption.
CITATION STYLE
Micciancio, D., & Schultz, M. (2023). Error Correction and Ciphertext Quantization in Lattice Cryptography. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 14085 LNCS, pp. 648–681). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-38554-4_21
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