Bridging Theory and Practice in Password-Based Cryptography

在线身份验证通常基于密码。虽然对基于密码的加密系统的安全界限的充分理解是设计健壮实例的先决条件，但仍存在尚未采用高级分析方法的系统。像多实例安全[1]这样的分析框架允许导出与基于密码的加密相关的安全边界。这个多实例示例从更高的抽象形式化了安全性-而不是关注单个实例的安全性，而是分析整个系统。这扩大了方法，允许对第二道防线进行分析。Bellare et. al. [1]是密码salting常见做法的正式安全证明。公开加盐不会影响对手恢复单个密码的优势，但会极大地影响恢复所有密码的优势。Bellare et.形式化的概念不可微的多实例情况下证明这一点。通过构建系统而没有更全面地理解安全概念，这些框架允许我们这样做，我们冒着错过简单安全改进的风险（如加盐）。现代攻击场景可能需要在多实例环境中预处理迭代的内存硬哈希字典。未来的场景可能涉及基于量子的攻击，具有在（平方根）n时间内搜索n长度列表的能力[2]。未来验证基于密码的密码系统将涉及考虑这些情况的联合。本项目的目的是将基于密码的密码学上下文的可证明安全性理论与野外使用的新的基于密码的协议的实例联系起来。这意味着三个目标，要线性接近：-进行研究到目前的景观基于密码的密码学。这意味着调查真实的生活中密码的产生和分布，以便根据经验结果产生一个模型。通过正式的安全分析评估模型的边界。- 考虑内存困难的预处理场景-为多实例情况构造一个紧密的安全界限。- 将边界推到在量子攻击者情况下保持舒适的水平，其中试图维护安全的各方是非量子的。

Online authentication is most often password-based. While a full understanding of the security bounds on password-based encryption systems is a precondition for designing robust instances, there exist systems which have yet to be subjected to advanced methods of analysis. Analytical frameworks like multi-instance security [1] allow for deriving security bounds relevant to password-based encryption. This multi-instance example formalises the security from a higher abstraction - instead of focusing of the security of a single instance, the system as a whole in analysed. This broadens the approach, allowing for analysis of second lines of defence. The example application from Bellare et. al. [1] is a formal security proof for the common practice of password salting. Public salting doesn't impact the adversary's advantage for recovering a single password, but greatly effects the advantage for recovering them all. Bellare et. al. formalised a conception of indifferentiability for a multi-instance case to prove this. By building systems without the fuller understanding of security conceptions, which these frameworks allow us, we run the risk of missing simple security improvements (like salting). A modern attack scenario could entail preprocessed dictionaries of iterated, memory-hard hashes in a multi-instance environment. Future scenarios could feasibly involve quantum based attacks, with the capability of searching n length lists in (square root) n time [2]. Future proofing password-based cryptographic systems will involve considering the union of these situations. Aims The aims of this project are intended to bridge the theory of provable security for the context of password based cryptography, with the instances of new password-based protocols used in the wild. This means three goals, to be approached linearly: -Conduct research into the current landscape of password-based cryptography. Which means investigating the generation and distribution of passwords in real life, in order to produce a model based on empirical results. Assess bounds for the model with formal security analysis. - Consider the memory-hard, preprocessed scenario - constructing a tight security bound for the multi-instance case. -Push bounds to levels which remain comfortable in the quantum attacker case, where the parties attempting to maintain security are non-quantum.