We derive the first adaptively secure identity-based encryption (\(\textsf {IBE} \)) and attribute-based encryption (\(\textsf {ABE} \)) for t-conjunctive normal form formula (t-CNF), and selectively secure \(\textsf {ABE} \) for general circuits from lattices, with \(1-o(1)\) leakage rates, in the both relative leakage model and bounded retrieval model (\(\textsf {BRM} \)). To achieve this, we first identify a new fine-grained security notion for \(\textsf {ABE} \)—partially adaptive/selective security, and instantiate this notion from the learning with errors (\(\textsf {LWE} \)) assumption. Then, by using this notion, we design a new key compressing mechanism for identity-based/attributed-based weak hash proof system (\(\textsf {IB} \)/\(\textsf {AB} \)-\(\textsf {wHPS} \)) for various policy classes, achieving (1) succinct secret keys and (2) adaptive/selective security matching the existing non-leakage resilient lattice-based designs. Using the existing connection between weak hash proof system and leakage resilient encryption, the succinct-key \(\textsf {IB} \)/\(\textsf {AB} \)-\(\textsf {wHPS} \) can yield the desired leakage resilient \(\textsf {IBE} \)/\(\textsf {ABE} \) schemes with the optimal leakage rates in the relative leakage model. Finally, by further improving the prior analysis of the compatible locally computable extractors, we can achieve the optimal leakage rates in the \(\textsf {BRM} \).

我们为t -conjunctive 范式公式 (t-CNF ) 推导了第一个自适应安全的基于身份的加密 ( \(\textsf {IBE} \) ) 和基于属性的加密 ( \(\textsf {ABE} \) ) ，并在相对泄漏模型和有界检索模型（\ ( \ textsf {BRM} \) )。为了实现这一目标，我们首先为\(\textsf {ABE} \)确定一个新的细粒度安全概念- 部分自适应/选择性安全性，并从错误学习中实例化这个概念 ( \(\textsf {LWE} \)） 假设。然后，利用这个概念，我们为基于身份/基于属性的弱哈希证明系统设计了一种新的密钥压缩机制（\(\textsf {IB} \) / \(\textsf {AB} \) - \(\ textsf {wHPS} \)）适用于各种策略类别，实现（1）简洁的密钥和（2）与现有的非泄漏弹性基于网格的设计相匹配的自适应/选择性安全性。利用弱哈希证明系统和泄漏弹性加密之间的现有连接，简洁密钥\(\textsf {IB} \) / \(\textsf {AB} \) - \(\textsf {wHPS} \) 可以产生所需的泄漏弹性\(\textsf {IBE} \) / (\textsf {ABE} \)方案，在相对泄漏模型中具有最佳泄漏率。最后，通过进一步改进兼容的本地可计算提取器的先验分析，我们可以在\(\textsf {BRM} \)中实现最佳泄漏率。