International Association for Cryptologic Research

International Association
for Cryptologic Research


Mark Schultz

ORCID: 0000-0001-5761-9662


Error Correction and Ciphertext Quantization in Lattice Cryptography
Mark Schultz Daniele Micciancio
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 $m \mapsto (q/2)m$ 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 $\Zset^k$, 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.


Daniele Micciancio (1)