Since the introduction of bcrypt in 1999, adaptive password hashing functions, whereby brute-force resistance increases symmetrically with computational difficulty for legitimate users, have been our most powerful post-breach countermeasure against credential disclosure. Unfortunately, the relatively low tolerance of users to added latency places an upper bound on the deployment of this technique in most applications. In this paper, we present a multi-factor credential hashing function (MFCHF) that incorporates the additional entropy of multi-factor authentication into password hashes to provide asymmetric resistance to brute-force attacks. MFCHF provides full backward compatibility with existing authentication software (e.g., Google Authenticator) and hardware (e.g., YubiKeys), with support for common usability features like factor recovery. The result is a 10^6 to 10^48 times increase in the difficulty of cracking hashed credentials, with little added latency or usability impact.

翻译：自1999年bcrypt问世以来，自适应密码哈希函数通过使暴力破解难度与合法用户计算开销呈对称增长，成为凭证泄露后最强大的防御机制。然而，用户对延迟增加的低容忍度限制了该技术在实际应用中的部署。本文提出一种多因子凭证哈希函数(MFCHF)，通过将多因子认证的额外熵纳入密码哈希计算，实现针对暴力攻击的非对称防护能力。MFCHF完全向后兼容现有认证软件（如Google Authenticator）和硬件（如YubiKeys），并支持因子恢复等常见可用性特性。实验表明，该方法可在几乎不增加延迟或降低可用性的前提下，将哈希凭证破解难度提升10^6至10^48倍。