实例化哈希-然后-评估范式:加强PRF,PCF和OPRF
Chris Brzuska1, Geoffroy Couteau2, Christoph Egger2,3
1Aalto University, Espoo, Finland.
概括
这项研究引入了一种新的方法来构建伪随机函数 (PRFs),通过用公钥和非自适应的PRF替换随机预言. 这种技术增强了多方计算和无意识的PRF应用程序的安全性.
科学领域:
- 密码学和信息安全信息安全
- 理论计算机科学 理论计算机科学
- 应用数学 应用数学 应用数学
背景情况:
- 哈希-然后-评估范式对于从较弱的原始构建伪随机函数 (PRF) 至关重要.
- 现有的构造通常依赖于公开的预处理随机预言 (ROs),这可能是计算密集的.
- 安全的多方计算 (MPC) 应用程序从PRF中受益,只有低复杂度的弱PRF (wPRF) 处理秘密依赖操作.
研究的目的:
- 为了实例化PRF的哈希-然后-评估范式,使用公钥和非适应性PRF而不是随机预言.
- 分析现有的弱PRF候选人的安全性,当他们的输入通过这种新的公共预处理方法生成时.
- 将这些结果扩展到无意识的PRF和伪随机相关函数 (PCF).
主要方法:
- 在PRF结构中用函数 `f(k_H, elf(x)) ` 取代了随机语句 (RO),其中 `f` 是一个非自适应的PRF,而 `k_H` 是一个公钥.
- 执行类似于现有方法的加密分析,利用"f"的伪随机性来确保良好的统计特性.
- 调查了对使用伪随机输入对wPRF的攻击对加密假设的影响,例如学习平价与噪声 (LPN) 问题.
主要成果:
- 证明了一些现有的弱PRF候选人在新建设下仍然具有可信的安全性.
- 表明,对由 `f` 生成的伪随机输入的wPRF的攻击可能意味着从高噪音LPN的硬度中获得关键协议.
- 成功地应用了转换,以获得遗忘PRF和PCF,PAKE,PSI和静音OT扩展的核心组件的结果.
结论:
- 拟议的转型是将RO预处理替换为公共的预处理,这种转型是有效的和广泛适用的.
- 这种方法保持了安全性,同时有可能减少MPC和相关加密协议中的计算复杂性.
- 这些发现为必不可少的加密原体,如忘记PRF和PCF提供了新的构造.
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