1970-01-01

(2026-08) Two-Limb CRT Ring-LWE Encryption with Exact Decryption and Public Re-randomization

• Damir Vodenicarevic
• Andrei Fleiser
• Pierre Seznec
• Karen Mayen Naranjo
• Lucas Foucher
• Léo Besançon
• Thybault Alabarbe
• Jean-François Morcillo
• Benjamin Reynes
• Lilian Urvoy

2026-08-05

• #cryptography
• #paper

Abstract

Anonymity infrastructures such as mix networks, anonymous storage, and privacy-preserving replication rely on public re-randomization: any party holding only public information can transform a ciphertext into a fresh-looking encryption of the same plaintext, hiding the linkage between the two. Classical ElGamal-based solutions are broken by quantum adversaries, while existing lattice-based alternatives carry very large ciphertexts with unanalyzed noise growth, rely on heavyweight homomorphic-encryption stacks with approximate (rounded) decryption, or lack a precise analysis of how many re-randomizations are safe. We address this gap with a practical Ring Learning with Errors (Ring-LWE) public-key encryption scheme supporting public re-randomization without ciphertext growth. Our construction is Lyubashevsky–Peikert–Regev / Fan–Vercauteren (LPR/BFV)-style encryption over $R=\mathbb{Z}[x]/(x^n+1)$ with $n=4096$, engineered around a two-limb Chinese Remainder Theorem (CRT) modulus $q=t\cdot q_2$ with 32-bit primes. Embedding plaintext as $\Delta M = q_2 M$ makes the message vanish modulo $q_2$, so the $q_2$-limb carries only the decryption noise, enabling exact message recovery without rounding. We prove correctness with explicit decryption-failure bounds that remain valid under repeated re-randomization, via an aggregation lemma showing that arbitrarily many re-randomizations affect decryption only through a single aggregated randomness triple. We also prove that two-limb ciphertexts are pseudorandom (indistinguishable from uniform, IND$) under Decision Ring-LWE over the combined modulus $q=tq_2$; security against chosen-plaintext attack (IND-CPA) and re-randomization unlinkability follow. A constant-time Rust implementation encrypts in 0.80 ms, re-randomizes in 0.51 ms, and decrypts in 0.21 ms per 64 KiB ciphertext carrying 15.5 KiB of payload on a fixed-frequency 3.8 GHz CPU—on par with a modulus-matched Microsoft SEAL baseline—and passes timing-leakage tests. Empirical noise simulations validate the analysis.