International Association
for Cryptologic Research

In the past three decades, an impressive body of knowledge has been built around secure and private password authentication. In particular, secure password-authenticated key exchange (PAKE) protocols require only minimal overhead over a classical Diffie-Hellman key exchange. PAKEs are also known to fulfill strong composable security guarantees that capture many password-specific concerns such as password correlations or password mistyping, to name only a few. However, to enjoy both round-optimality and strong security, applications of PAKE protocols must provide \emph{unique} session and participant identifiers. If such identifiers are not readily available, they must be agreed upon at the cost of additional communication flows, a fact which has been met with incomprehension among practitioners, and which hindered the adoption of provably secure password authentication in practice. In this work, we resolve this issue by proposing a new paradigm for truly \emph{password-only} yet securely composable PAKE, called \emph{bare} PAKE. We formally prove that two prominent PAKE protocols, namely CPace and EKE, can be cast as bare PAKEs and hence do not require pre-agreement of anything else than a password. Our bare PAKE modeling further allows us to investigate a novel ``reusability'' property of PAKEs, i.e., whether $n^2$ pairwise keys can be exchanged from only $n$ messages, just as the Diffie-Hellman non-interactive key exchange can do in a public-key setting. As a side contribution, this add-on property of bare PAKEs leads us to observe that some previous PAKE constructions relied on unnecessarily strong, ``reusable'' building blocks. By showing that ``non-reusable'' tools suffice for standard PAKE, we open a new path towards round-optimal post-quantum secure password-authenticated key exchange.

We revisit the notion of Threshold Password-Authenticated Key Exchange (tPAKE), and we extend it to augmented tPAKE (atPAKE), which protects password information even in case of compromise of all servers, except for allowing an (inevitable) offline dictionary attack. Compared to prior notions of tPAKE this is analogous to replacing symmetric PAKE, where the server stores the user’s password, with an augmented (or asymmetric) PAKE, like OPAQUE [39], where the server stores a password hash, which can be used only as a target in an offline dictionary search for the password. An atPAKE scheme also strictly improves on security of an aPAKE, by secret-sharing the password hash among a set of servers. Indeed, our atPAKE protocol is a natural realization of threshold OPAQUE. We formalize atPAKE in the framework of Universal Composability (UC), and show practical ways to realize it. All our schemes are generic compositions which interface to any aPAKE used as a sub-protocol, making them easier to adopt. Our main scheme relies on threshold Oblivious Pseudorandom Function (tOPRF), and our independent contribution fixes a flaw in the UC tOPRF notion of [36] and upgrades the tOPRF scheme therein to achieve the fixed definition while preserving its minimal cost and round complexity. The technique we use enforces implicit agreement on arbitrary context information within threshold computation, and it is of general interest.

Driven by the NIST's post-quantum standardization efforts and the selection of Kyber as a lattice-based Key-Encapsulation Mechanism (KEM), several Password Authenticated Key Exchange (PAKE) protocols have been recently proposed that leverage a KEM to create an efficient, easy-to-implement and secure PAKE. In two recent works, Beguinet et al. (ACNS 2023) and Pan and Zeng (ASIACRYPT 2023) proposed generic compilers that transform KEM into PAKE, relying on an Ideal Cipher (IC) defined over a group. However, although IC on a group is often used in cryptographic protocols, special care must be taken to instantiate such objects in practice, especially when a low-entropy key is used. To address this concern, Dos Santos et al. (EUROCRYPT 2023) proposed a relaxation of the IC model under the Universal Composability (UC) framework called Half-Ideal Cipher (HIC). They demonstrate how to construct a UC-secure PAKE protocol, EKE-KEM, from a KEM and a modified 2-round Feistel construction called m2F. Remarkably, the m2F sidesteps the use of an IC over a group, and instead employs an IC defined over a fixed-length bitstring domain, which is easier to instantiate. In this paper, we introduce a novel PAKE protocol called CHIC that improves the communication and computation efficiency of EKE-KEM, by avoiding the HIC abstraction. Instead, we split the KEM public key in two parts and use the m2F directly, without further randomization. We provide a detailed proof of the security of CHIC and establish precise security requirements for the underlying KEM, including one-wayness and anonymity of ciphertexts, and uniformity of public keys. Our findings extend to general KEM-based EKE-style protocols and show that a passively secure KEM is not sufficient. In this respect, our results align with those of Pan and Zeng (ASIACRYPT 2023), but contradict the analyses of KEM-to-PAKE compilers by Beguinet et al. (ACNS 2023) and Dos Santos et al. (EUROCRYPT 2023). Finally, we provide an implementation of CHIC, highlighting its minimal overhead compared to the underlying KEM -- Kyber. An interesting aspect of the implementation is that we reuse the rejection sampling procedure in Kyber reference code to address the challenge of hashing onto the public key space. As of now, to the best of our knowledge, CHIC stands as the most efficient PAKE protocol from black-box KEM that offers rigorously proven UC security.

We witness 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 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 scheme (aptSIG) 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, namely that compromising even all n servers also does not leak any information, except via an unavoidable ODA attack, which reveals the key (and the password) 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 [12] and a UC augmented Password-Protected Secret Sharing (aPPSS), which we define as an extension of prior notion of PPSS [26]. As concrete instantiations we obtain secure aptSIG schemes for ECDSA and BLS signatures with very small overhead over the respective respective threshold signature.

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 more general and it includes the formalization of components that are needed in the analysis of TLS-EA 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.

An Ideal Cipher (IC) is a cipher where each key defines a random permutation on the domain. Ideal Cipher on a group has many attractive applications, e.g., the Encrypted Key Exchange (EKE) protocol for Password Authenticated Key Exchange (PAKE) [8], or asymmetric PAKE (aPAKE) [33, 31]. However, known constructions for IC on a group domain all have drawbacks, including key leakage from timing information [12], requiring 4 hash-onto-group operations if IC is an 8-round Feistel [22], and limiting the domain to half the group [9] or using variable-time encoding [47, 39] if IC is implemented via (quasi-) bijections from groups to bitstrings [33]. We propose an IC relaxation called a (Randomized) Half-Ideal Cipher (HIC), and we show that HIC on a group can be realized by a modified 2-round Feistel (m2F), at a cost of 1 hash-onto-group operation, which beats existing IC constructions in versatility and computational cost. HIC weakens IC properties by letting part of the ciphertext be non-random, but we exemplify that it can be used as a drop-in replacement for IC by showing that EKE [8] and aPAKE of [33] realize respectively UC PAKE and UC aPAKE even if they use HIC instead of IC. The m2F construction can also serve as IC domain extension, because m2F constructs HIC on domain D from an RO-indifferentiable hash onto D and an IC on 2κ-bit strings, for κ a security parameter. One application of such extender is a modular lattice-based UC PAKE using EKE instantiated with HIC and anonymous lattice-based KEM.

Von Ahn, Hopper and Langford introduced the notion of steganographic a.k.a. covert computation, to capture distributed computation where the attackers must not be able to distinguish honest parties from entities emitting random bitstrings. This indistinguishability should hold for the duration of the computation except for what is revealed by the intended outputs of the computed functionality. An important case of covert computation is mutually authenticated key exchange, a.k.a.\ mutual authentication. Mutual authentication is a fundamental primitive often preceding more complex secure protocols used for distributed computation. However, standard authentication implementations are not covert, which allows a network adversary to target or block parties who engage in authentication. Therefore, mutual authentication is one of the premier use cases of covert computation and has numerous real-world applications, e.g., for enabling authentication over steganographic channels in a network controlled by a discriminatory entity. We improve on the state of the art in covert authentication by presenting a protocol that retains covertness and security under concurrent composition, has minimal message complexity, and reduces protocol bandwidth by an order of magnitude compared to previous constructions. To model the security of our scheme we develop a UC model, which captures the standard features of secure mutual authentication but extends them to covertness. We prove our construction secure in this UC model. We also provide a proof-of-concept implementation of our scheme.

In Crypto'21 Gu, Jarecki, and Krawczyk [20] 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. In this paper we show two aPAKE protocols that achieve optimal computational cost and optimal round complexity. Our protocols can be seen as applications of the Encrypted Key Exchange (EKE) compiler of Bellovin and Merritt [6], 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 applying password-encryption to messages of a unilaterally authenticated Key Exchange (ua-KE). We present two versions of this compiler. The first uses salted password hash and takes 3 rounds if the client initiates. The second uses unsalted password hash and takes a single simultaneous flow (it is the first aPAKE to do so), thus simultaneously matching the minimal computational cost and the minimal round complexity of PAKE and KE. We analyze our aPAKE protocols assuming Ideal Cipher (IC) on a group as modular constructions from ua-KE realized via a (universally composable) Authenticated Key Exchange where the server uses one-time keys (otk-AKE). We then show that one-pass variants of 3DH and HMQV securely realize otk-AKE in ROM. Interestingly, the two resulting concrete aPAKE's use the exact same protocol messages as two natural variants of EKE, and the only difference between the symmetric PAKE (EKE) and asymmetric PAKE (our protocols) is in the key derivation equation used to derive the final session key output.

Oblivious Pseudorandom Function (OPRF) is a protocol between a client holding input x and a server holding key k for a PRF F. At the end, the client learns F_k(x) and nothing else while the server learns nothing. OPRF's have found diverse applications as components of larger protocols, and the currently most efficient instantiation, with security proven in the UC model, is F_k(x)=H2(x,(H1(x))^k) computed using so-called exponential blinding, i.e., the client sends a=(H1(x))^r for random r, the server responds b=a^k, which the client ublinds as v=b^{1/r} to compute F_k(x)=H2(x,v). However, this protocol requires two variable-base exponentiations on the client, while a more efficient multiplicative blinding scheme replaces one or both client exponentiations with fixed-base exponentiation, leading to the decrease of the client's computational cost by a factor between two to six, depending on pre-computation. We analyze the security of the above OPRF with multiplicative blinding, showing surprising weaknesses that offer attack avenues which are not present using exponential blinding. We characterize the security of this OPRF implementation as a "Revised OPRF" functionality, a relaxation of UC OPRF functionality used in prior work. On the positive side, we show that the Revised OPRF suffices for the security of OPAQUE, the asymmetric PAKE protocol, hence allowing OPAQUE the computational advantages of multiplicative blinding. Unfortunately, we also show examples of other OPRF applications which become insecure when using such blinding. The conclusion is that usage of multiplicative blinding for F_k(x) defined as above, in settings where correct value g^k (needed for multiplicative blinding) is not authenticated, and OPRF inputs are of low entropy, must be carefully analyzed, or avoided all together. We complete the picture by showing a simple and safe alternative definition of function F_k(x) which offers (full) UC OPRF security using either form of blinding.

OPAQUE [Jarecki et al., Eurocrypt 2018] is an asymmetric password authenticated key exchange (aPAKE) protocol that is being developed as an Internet standard and for use within TLS 1.3. OPAQUE combines an Oblivious PRF (OPRF) with an authenticated key exchange to provide strong security properties, including security against pre-computation attacks (called saPAKE security). However, the security of OPAQUE relies crucially on the integrity of the OPRF. If the latter breaks (by cryptanalysis, quantum attacks or security compromise), the user's password is immediately exposed to an offline dictionary attack. To address this weakness, we present KHAPE, a variant of OPAQUE that does not require the use of an OPRF to achieve aPAKE security, resulting in improved resilience and performance. An OPRF can be optionally added to KHAPE, for enhanced saPAKE security, but without opening the password to an offline dictionary attack upon OPRF compromise. In addition to resilience to OPRF compromise, a DH-based implementation of KHAPE (using HMQV) offers the best performance among aPAKE protocols in terms of exponentiations with less than the cost of an exponentiation on top of an unauthenticated Diffie-Hellman exchange. KHAPE uses three messages with explicit client authentication and four with explicit server authentication (one more than OPAQUE in the latter case). All results in the paper are proven within the UC framework in the ideal cipher model. Of independent interest is our treatment of "key-hiding AKE" which KHAPE uses as a main component, and our UC proofs of AKE security for protocols 3DH (a basis of Signal) and HMQV that we use as efficient instantiations of KHAPE.

Protocols for password authenticated key exchange (PAKE) allow two parties who share only a weak password to agree on a cryptographic key. We revisit the notion of PAKE in the universal composability (UC) framework, and propose a relaxation of the PAKE functionality of Canetti et al. that we call lazy-extraction PAKE (lePAKE). Our relaxation allows the ideal-world adversary to postpone its password guess until after a session is complete. We argue that this relaxed notion still provides meaningful security in the password-only setting. As our main result, we show that several PAKE protocols that were previously only proven secure with respect to a ``game-based'' definition of security can be shown to UC-realize the lePAKE functionality in the random-oracle model. These include SPEKE, SPAKE2, and TBPEKE, the most efficient PAKE schemes currently known.

We initiate a study of \emph{pseudorandom encodings}: efficiently computable and decodable encoding functions that map messages from a given distribution to a random-looking distribution. For instance, every distribution that can be perfectly compressed admits such a pseudorandom encoding. Pseudorandom encodings are motivated by a variety of cryptographic applications, including password-authenticated key exchange, ``honey encryption'' and steganography. The main question we ask is whether \emph{every} efficiently samplable distribution admits a pseudorandom encoding. Under different cryptographic assumptions, we obtain positive and negative answers for different flavors of pseudorandom encodings, and relate this question to problems in other areas of cryptography. In particular, by establishing a two-way relation between pseudorandom encoding schemes and efficient invertible sampling algorithms, we reveal a connection between adaptively secure multi-party computation and questions in the domain of steganography.

Password-Authenticated Key Exchange (PAKE) protocols allow two parties that share a password to establish a shared key in a way that is immune to offline attacks. Asymmetric PAKE (aPAKE) [20] adapts this notion to the common client-server setting, where the server stores a one-way hash of the password instead of the password itself, and server compromise allows the adversary to recover the password only via the (inevitable) offline dictionary attack. Most aPAKE protocols, however, allow an attacker to pre-compute a dictionary of hashed passwords, thus instantly learning the password on server compromise. Recently, Jarecki, Krawczyk, and Xu formalized a Universally Composable strong aPAKE (saPAKE) [23], which requires the password hash to be salted so that the dictionary attack can only start after the server compromise leaks the salt and the salted hash. The UC saPAKE protocol shown in [23], called OPAQUE, uses 3 protocol flows, 3–4 exponentiations per party, and relies on the One-More Diffie-Hellman assumption in ROM.We propose an alternative UC saPAKE construction based on a novel use of the encryption+SPHF paradigm for UC PAKE design [19, 26]. Compared to OPAQUE, our protocol uses only 2 flows, has comparable costs, avoids hashing onto a group, and relies on different assumptions, namely Decisional Diffie-Hellman (DDH), Strong Diffie-Hellman (SDH), and an assumption that the Boneh-Boyen function $$f_ s (x)=g^{1/( s +x)}$$ [9] is a Salted Tight One-Way Function (STOWF). We formalize a UC model for STOWF and analyze the Boneh-Boyen function as UC STOWF in the generic group model and ROM.Our saPAKE protocol employs a new form of Conditional Key Encapsulation Mechanism (CKEM), a generalization of SPHF, which we call an implicit-statement CKEM. This strengthening of SPHF allows for a UC (sa)PAKE design where only the client commits to its password, and only the server performs an SPHF, compared to the standard UC PAKE design paradigm where the encrypt+SPHF subroutine is used symmetrically by both parties.

Covert computation strengthens secure computation by hiding not only participants’ inputs (up to what the protocol outputs reveal), but also the fact of computation taking place (up to the same constraint). Existing maliciously-secure covert computation protocols are orders of magnitude more costly than non-covert secure computation, and they are either non-constant round [5] or they use non-black-box simulation [10]. Moreover, constant-round covert computation with black-box simulation is impossible in the plain model [10].We show that constant-round Covert Two-Party Computation (2PC) of general functions secure against malicious adversaries is possible with black-box simulation under DDH in the Common Reference String (CRS) model, where the impossibility result of [10] does not apply. Moreover, our protocol, a covert variant of a “cut-and-choose over garbled circuits” approach to constant-round 2PC, is in the same efficiency ballpark as standard, i.e. non-covert, 2PC protocols of this type. In addition, the proposed protocol is covert under concurrent self-composition.An essential tool we use is a covert simulation-sound Conditional KEM (CKEM) for arithmetic languages in prime-order groups, which we realize in CRS or ROM at costs which are either the same (in ROM) or very close (in CRS) to known HVZK’s for such languages.

We present a secure two-factor authentication (TFA) scheme based on the possession by the user 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 PAKE, defined by Jarecki et al., and any Short Authenticated String (SAS) Message Authentication, defined by Vaudenay. We show an efficient instantiation the modular, generic construction we give is not PAKE-agnostic because it doesn’t even use PAKE, but the instantiation of this scheme which instantiates DE-PAKE with PTR+PAKE is PAKE-agnostic as you say 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.