Key Encapsulation Mechanisms (KEMs) are a set of cryptographic techniques that are designed to provide symmetric encryption key using asymmetric mechanism (public key). In the current study, we concentrate on design and analysis of key encapsulation mechanism from low density lattice codes (KEM-LDLC) to go down the key size by keeping an acceptable level of security. The security of the proposed KEM-LDLC relies on the difficulty of solving the closest vector problem (CVP) and the shortest basis problem (SBP) of the lattices. Furthermore, this paper discusses other performance analyses results such as key size, error performance, and computational complexity, as well as conventional security analysis against applied attacks. Reducing the key size is performed by two approaches: (i) saving the generation sequence of the latin square LDLCs parity-check matrix of as a part of the secret key set; (ii) using the hermite normal form (HNF) of the latin square LDLCs generator matrix as part of the public key set. These enhancements enable us to attain greater efficiency and security compared to earlier code-based KEMs.

翻译：密钥封装机制（KEMs）是一类密码学技术，旨在通过非对称机制（公钥）提供对称加密密钥。本研究聚焦于基于低密度格码的密钥封装机制（KEM-LDLC）的设计与分析，以在保持可接受安全水平的同时降低密钥尺寸。所提出的KEM-LDLC的安全性依赖于格上最近向量问题（CVP）与最短基问题（SBP）的求解困难性。此外，本文讨论了其他性能分析结果，包括密钥尺寸、误码性能、计算复杂度，以及针对实际攻击的传统安全性分析。密钥尺寸的缩减通过两种方法实现：（i）将拉丁方LDLC奇偶校验矩阵的生成序列作为私钥集的一部分保存；（ii）使用拉丁方LDLC生成矩阵的埃尔米特标准型（HNF）作为公钥集的一部分。这些改进使得本方案相较于早期的基于编码的KEMs能够实现更高的效率与安全性。