Paper 2026/1350

Refined Evaluation Methods of Decryption Failure Rate in Lattice-Based Public-Key Encryption with Message Encoding

Abstract

Lattice-based cryptography is one of the most promising candidates for post-quantum cryptography. Decryption Failure Rate (DFR) is a critical metric for the correctness and security of lattice-based public-key encryption (PKE) schemes. At present, most DFR evaluation methods for lattice-based PKE with message encoding rely on oversimplified assumptions, rough approximations, and fail to fully exploit the geometric structure of special encoding lattices, resulting in loose or inaccurate bounds. To address these limitations, this paper proposes a refined DFR evaluation framework for lattice-based PKE with message encoding, focusing on two mainstream decoding paradigms: Maximum Likelihood Decoding (MLD) and Bounded Distance Decoding (BDD). For MLD-based schemes, we precisely characterize the minimal vectors of Barnes-Wall (BW) lattices and derive tighter union bounds by leveraging the encoding lattice structure. For BDD-based schemes, we introduce a noncentral chi-squared distribution based method to model mixed noise composed of Gaussian and discrete components, avoiding the inaccuracy of conventional pure Gaussian approximations. Furthermore, we extend the framework to algebraic-lattice-based PKE by analyzing the variance and correlation of polynomial product coefficients, and propose a weighted chi-squared distribution with saddlepoint approximation to handle correlated coefficients. We validate the proposed methods on representative lattice-based PKEs including CNTR, \scloud, and CNTR-Prime, resulting in the DFR upper bound approximate 15 bits decreasing for CNTR, 1 bit decreasing for \scloud, and at least 84 bits increasing for CNTR-Prime. The experimental results show that our refined analysis yields significantly tighter and more accurate DFR bounds compared with traditional approaches, providing a reliable theoretical basis for parameter selection and security certification of practical lattice-based cryptosystems.