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We witness an increase in applications like cryptocurrency wallets, which involve users issuing signatures using private keys. To protect these keys from loss or compromise, users commonly outsource them to a custodial server. This creates a new point of failure, because compromise of such a server leaks the user’s key, and if user authentication is implemented with a password then this password becomes open to an offline dictionary attack (ODA). A better solution is to secret-share the key among a set of servers, possibly including user’s own device(s), and implement password authentication and signature computation using threshold cryptography. We propose a notion of augmented password-protected threshold signature (aptSIG) scheme which captures the best possible security level for this setting. Using standard threshold cryptography techniques, i.e. threshold password authentication and threshold signatures, one can guarantee that compromising up to t out of n servers reveals no information on either the key or the password. However, we extend this with a novel property, that compromising even all n servers also does not leak any information, except via an unavoidable ODA attack, which reveals the key only if the attacker guesses the password. We define aptSIG in the Universally Composable (UC) framework and show that it can be constructed very efficiently, using a black-box composition of any UC threshold signature [13] and a UC augmented Password-Protected Secret Sharing (aPPSS), which we define as an extension of prior notion of PPSS [30]. As concrete instantiations we obtain secure aptSIG schemes for ECDSA (in the case of t=n-1) and BLS signatures with very small overhead over the respective threshold signature. Finally, we note that both the notion and our generic solution for augmented password-protected threshold signatures can be generalized to password-protecting MPC for any keyed functions. 

OPAQUE is an Asymmetric Password-Authenticated Key Exchange (aPAKE) protocol being standardized by the IETF (Internet Engineering Task Force) as a more secure alternative to the traditional “password-over-TLS” mechanism prevalent in current practice. OPAQUE defends against a variety of vulnerabilities of password-over-TLS by dispensing with reliance on PKI and TLS security, and ensuring that the password is never visible to servers or anyone other than the client machine where the password is entered. In order to facilitate the use of OPAQUE in practice, integration of OPAQUE with TLS is needed. The main proposal for standardizing such integration uses the Exported Authenticators (TLS-EA) mechanism of TLS 1.3 that supports post-handshake authentication and allows for a smooth composition with OPAQUE. We refer to this composition as TLS-OPAQUE and present a detailed security analysis for it in the Universal Composability (UC) framework. Our treatment is general and includes the formalization of components that are needed in the analysis of TLS-OPAQUE but are of wider applicability as they are used in many protocols in practice. Specifically, we provide formalizations in the UC model of the notions of post-handshake authentication and channel binding. The latter, in particular, has been hard to implement securely in practice, resulting in multiple protocol failures, including major attacks against prior versions of TLS. Ours is the first treatment of these notions in a computational model with composability guarantees. We complement the theoretical work with a detailed discussion of practical considerations for the use and deployment of TLS-OPAQUE in real-world settings and applications. 

In Crypto’21 Gu, Jarecki, and Krawczyk [25] showed an asymmetric password authenticated key exchange protocol (aPAKE) whose computational cost matches (symmetric) password authenticated key exchange (PAKE) and plain (i.e. unauthenticated) key exchange (KE). However, this minimal-cost aPAKE did not match prior aPAKE’s in round complexity, using 4 rounds assuming the client initiates compared to 2 rounds in an aPAKE of Bradley et al. [13]. In this paper we show two aPAKE protocols (but not strong aPAKEs like [13, 30]), which achieve optimal computational cost and optimal round complexity. Our protocols can be seen as variants of the Encrypted Key Exchange (EKE) compiler of Bellovin and Merritt [7], which creates password-authenticated key exchange by password-encrypting messages in a key exchange protocol. Whereas Bellovin and Merritt used this method to construct a PAKE by applying password-encryption to KE messages, we construct an aPAKE by password-encrypting messages of a unilaterally authenticated Key Exchange (ua-KE). We present two versions of this compiler. The first uses salted password hash and takes 2 rounds if the server initiates. The second uses unsalted password hash and takes a single simultaneous flow, thus simultaneously matching the minimal computational cost and the minimal round complexity of PAKE and KE. We analyze our aPAKE protocols assuming an Ideal Cipher (IC) on a group, and we analyze them as modular constructions from ua-KE realized via a universally composable Authenticated Key Exchange where the server uses one-time keys (otk-AKE). We also show that one-pass variants of 3DH and HMQV securely realize otk-AKE in the ROM. Interestingly, the two resulting concrete aPAKE’s use the exact same protocol messages as variants of EKE, and the only difference between the symmetric PAKE (EKE) and asymmetric PAKE (our protocols) is in the key derivation equation. 

We present a secure two-factor authentication (TFA) scheme based on the user’s possession of a password and a crypto-capable device. Security is “end-to-end” in the sense that the attacker can attack all parts of the system, including all communication links and any subset of parties (servers, devices, client terminals), can learn users’ passwords, and perform active and passive attacks, online and offline. In all cases the scheme provides the highest attainable security bounds given the set of compromised components. Our solution builds a TFA scheme using any Device-enhanced Password-authenticated Key Exchange (PAKE), defined by Jarecki et al., and any Short Authenticated String (SAS) Message Authentication, defined by Vaudenay. We show an efficient instantiation of this modular construction, which utilizes any password-based client-server authentication method, with or without reliance on public-key infrastructure. The security of the proposed scheme is proven in a formal model that we formulate as an extension of the traditional PAKE model. We also report on a prototype implementation of our schemes, including TLS-based and PKI-free variants, as well as several instantiations of the SAS mechanism, all demonstrating the practicality of our approach. Finally, we present a usability study evaluating the viability of our protocol contrasted with the traditional PIN-based TFA approach in terms of efficiency, potential for errors, user experience, and security perception of the underlying manual process. 1