We analyse a two password-authenticated key exchange protocols, a variant of CPace and a protocol related to the well-known SRP protocol. Our security results are tight. The first result gives us some information about trade-offs for design choices in CPace. The second result provides information about the security of SRP. Our analysis is done in a new game-based security definition for password-authenticated key exchange. Our definition accomodates arbitrary password sampling...

We show the Seyhan-Akleylek key exchange protocol [J. Supercomput., 2023, 79:17859-17896] cannot resist offline dictionary attack and impersonation attack, not as claimed.

Fuzzy password authenticated key exchange (fuzzy PAKE) protocols enable two parties to securely exchange a session-key for further communication. The parties only need to share a low entropy password. The passwords do not even need to be identical, but can contain some errors. This may be due to typos, or because the passwords were created from noisy biometric readings. In this paper we provide an overview and comparison of existing fuzzy PAKE protocols. Furthermore, we analyze certain...

In this paper, we construct the first password authenticated key exchange (PAKE) scheme from isogenies with Universal Composable (UC) security in the random oracle model (ROM). We also construct the first two PAKE schemes with UC security in the quantum random oracle model (QROM), one is based on the learning with error (LWE) assumption, and the other is based on the group-action decisional Diffie- Hellman (GA-DDH) assumption in the isogeny setting. To obtain our UC-secure PAKE scheme in...

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to agree upon a cryptographic key, in the setting where the only secret shared in advance is a low-entropy password. The standard security notion for PAKE is in the Universal Composability (UC) framework. In recent years there have been a large number of works analyzing the UC-security of Encrypted Key Exchange (EKE), the very first PAKE protocol, and its One-encryption variant (OEKE), both of which compile an...

Driven by the NIST's post-quantum standardization efforts and the selection of $\mathsf{Kyber}$ 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)...

Decoy accounts are often used as an indicator of the compromise of sensitive data, such as password files. An attacker targeting only specific known-to-be-real accounts might, however, remain undetected. A more effective method proposed by Juels and Rivest at CCS'13 is to maintain additional fake passwords associated with each account. An attacker who gains access to the password file is unable to tell apart real passwords from fake passwords, and the attempted usage of a false password...

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...

IDentity-based Password Authentication and Key Establishment (ID-PAKE) is an interesting trade-off between the security and efficiency, specially due to the removal of costly Public Key Infrastructure (PKI). However, we observe that previous PAKE schemes such as Beguinet et al. (ACNS 2023), Pan et al. (ASIACRYPT 2023) , Abdallah et al. (CRYPTO 2020) etc. fail to achieve important security properties such as weak/strong Perfect Forward Secrecy (s-PFS), user authentication and resistance to...

Password-Authenticated Key Exchange (PAKE) allows two parties to establish a common high-entropy secret from a possibly low-entropy pre-shared secret such as a password. In this work, we provide the first PAKE protocol with subversion resilience in the framework of universal composability (UC), where the latter roughly means that UC security still holds even if one of the two parties is malicious and the honest party's code has been subverted (in an undetectable manner). We achieve this...

The KHAPE-HMQV protocol is a state-of-the-art highly efficient asymmetric password-authenticated key exchange protocol that provides several desirable security properties, but has the drawback of being vulnerable to quantum adversaries due to its reliance on discrete logarithm-based building blocks: solving a single discrete logarithm allows the attacker to perform an offline dictionary attack and recover the password. We show how to modify KHAPE-HMQV to make the protocol quantum-annoying: a...

This paper analyses the Secure Remote Password Protocol (SRP) in the context of provable security. SRP is an asymmetric Password-Authenticated Key Exchange (aPAKE) protocol introduced in 1998. It allows a client to establish a shared cryptographic key with a server based on a password of potentially low entropy. Although the protocol was part of several standardization efforts, and is deployed in numerous commercial applications such as Apple Homekit, 1Password or Telegram, it still lacks a...

Password-authenticated key exchange (PAKE) is a class of protocols enabling two parties to convert a shared (possibly low-entropy) password into a high-entropy joint session key. Strong asymmetric PAKE (saPAKE), an extension that models the client-server setting where servers may store a client's password for repeated authentication, was the subject of standardization efforts by the IETF in 2019-20. In this work, we present the most computationally efficient saPAKE protocol so far: a...

Fuzzy Password-Authenticated Key Exchange (fuzzy PAKE) allows cryptographic keys to be generated from authentication data that is both fuzzy and of low entropy. The strong protection against offline attacks offered by fuzzy PAKE opens an interesting avenue towards secure biometric authentication, typo-tolerant password authentication, and automated IoT device pairing. Previous constructions of fuzzy PAKE are either based on Error Correcting Codes (ECC) or generic multi-party computation...

We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs), to allow instantiations with post-quantums KEM like KYBER. The ACNS23 paper left as an open problem to argue security against quantum attackers, with its security proof being in the universal composability (UC) framework. This is common for PAKE, however, at the time of this submission’s writing, it was not known how to prove (computational)...

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is oneway secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman...

Video conferencing apps like Zoom have hundreds of millions of daily users, making them a high-value target for surveillance and subversion. While such apps claim to achieve some forms of end-to-end encryption, they usually assume an incorruptible server that is able to identify and authenticate all the parties in a meeting. Concretely this means that, e.g., even when using the “end-to-end encrypted” setting, malicious Zoom servers could eavesdrop or impersonate in arbitrary groups. In...

We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), $\mathsf{PRF}(k, x) := \mathsf{wPRF}(k, \mathsf{RO}(x))$, which builds a PRF $\mathsf{PRF}$ from a weak PRF $\mathsf{wPRF}$ via a public preprocessing random oracle $\mathsf{RO}$. In applications to secure multiparty computation (MPC), only the low-complexity wPRF performs secret-depending operations. Our construction replaces RO by $f(k_H , \mathsf{elf}(x))$, where $f$ is a non-adaptive PRF and the key $k_H$...

We present Owl, an augmented password-authenticated key exchange (PAKE) protocol that is both efficient and supported by security proofs. Owl is motivated by recognized limitations in SRP-6a and OPAQUE. SRP-6a is the only augmented PAKE that has enjoyed wide use in practice to date, but it lacks the support of formal security proofs, and does not support elliptic curve settings. OPAQUE was proposed in 2018 as a provably secure and efficient alternative to SRP-6a, and was chosen by the IETF...

Password Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports. With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would...

Wireless-channel key exchange (WiKE) protocols that leverage Physical Layer Security (PLS) techniques could become an alternative solution for secure communication establishment, such as vehicular ad-hoc networks, wireless IoT networks, or cross-layer protocols. In this paper, we provide a novel abstraction of WiKE protocols and present the first game-based security model for WiKE. Our result enables the analysis of security guarantees offered by these cross-layer protocols and allows the...

Motivated by applications to the internet of things (IoT), Cremers, Naor, Paz, and Ronen (CRYPTO '22) recently considered a setting in which multiple parties share a common password and want to be able to pairwise authenticate. They observed that using standard password-authenticated key exchange (PAKE) protocols in this setting allows for catastrophic impersonation attacks whereby compromise of a single party allows an attacker to impersonate any party to any other. To address this, they...

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) [10], or asymmetric PAKE (aPAKE) [40, 36]. However, known constructions for IC on a group domain all have drawbacks, including key leakage from timing information [15], requiring 4 hash-onto-group operations if IC is an 8-round Feistel [27], and...

(Asymmetric) Password-based Authenticated Key Exchange ((a)PAKE) protocols allow two parties establish a session key with a pre-shared low-entropy password. In this paper, we show how Encrypted Key Exchange (EKE) compiler [Bellovin and Merritt, S&P 1992] meets tight security in the Universally Composable (UC) framework. We propose a strong 2DH variant of EKE, denoted by 2DH-EKE, and prove its tight security in the UC framework based on the CDH assumption. The efficiency of 2DH-EKE is...

The use of traditional cryptography based on symmetric keys has been replaced with the revolutionary idea discovered by Diffie and Hellman in 1976 that fundamentally changed communication systems by ensuring a secure transmission of information over an insecure channel. Nowadays public key cryptography is frequently used for authentication in e-commerce, digital signatures and encrypted communication. Most of the public key cryptosystems used in practice are based on integer factorization...

Secure computation is a cornerstone of modern cryptography and a rich body of research is devoted to understanding its round complexity. In this work, we consider two-party computation (2PC) protocols (where both parties receive output) that remain secure in the realistic setting where many instances of the protocol are executed in parallel (concurrent security). We obtain a two-round concurrent-secure 2PC protocol based on a single, standard, post-quantum assumption: The subexponential...

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to agree upon a cryptographic key, when the only information shared in advance is a low-entropy password. The standard security notion for PAKE (Canetti et al., Eurocrypt 2005) is in the Universally Composable (UC) framework. We show that unlike most UC security notions, UC PAKE does not imply correctness. While Canetti et al. has briefly noticed this issue, we present the first comprehensive study of correctness in UC...

We present two provably secure password-authenticated key exchange (PAKE) protocols based on a commutative group action. To date the most important instantiation of isogeny-based group actions is given by CSIDH. To model the properties more accurately, we extend the framework of cryptographic group actions (Alamati et al., ASIACRYPT 2020) by the ability of computing the quadratic twist of an elliptic curve. This property is always present in the CSIDH setting and turns out to be crucial in...

Password-authenticated key exchange (PAKE) is a major area of cryptographic protocol research and practice. Many PAKE proposals have emerged in the 30 years following the original 1992 Encrypted Key Exchange (EKE), some accompanied by new theoretical models to support rigorous analysis. To reduce confusion and encourage practical development, major standards bodies including IEEE, ISO/IEC and the IETF have worked towards standardizing PAKE schemes, with mixed results. Challenges have...

In this paper, we study the round complexity of concurrently secure computation protocols in the plain model, without random oracles or assuming the presence of a trusted setup. In the plain model, it is well known that concurrently secure two-party computation with polynomial simulation is impossible to achieve in two rounds. For this reason, we focus on the well-studied notion of security with super-polynomial simulation (SPS). Our main result is the first construction of two-round SPS...

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 security of the OPRF. If the latter breaks (by cryptanalysis,...

From June 2019 to March 2020, IETF conducted a selection process to choose password authenticated key exchange (PAKE) protocols for standardization. Similar standardization efforts were conducted before by IEEE (P1362.2) and ISO/IEC (11770-4). An important hallmark for this IETF selection process is its openness: anyone can nominate any candidate; all reviews are public; all email discussions on the IETF mailing lists are archived and publicly readable. However, despite the openness, it is...

The J-PAKE protocol is a Password Authenticated Key Establishment protocol whose security rests on Diffie-Hellman key establishment and Non-Interactive Zero Knowledge proofs. It has seen widespread deployment and has previously been proven secure, including forward secrecy, in a game-based model. In this paper we show that this earlier proof can be re-cast in the Universal Composability framework, thus yielding a stronger result. We also investigate the extension of such proofs to a...

During the Crypto Forum Research Group (CFRG)'s standardization of password-authenticated key exchange (PAKE) protocols, a novel property emerged: a PAKE scheme is said to be ``quantum-annoying'' if a quantum computer can compromise the security of the scheme, but only by solving one discrete logarithm for each guess of a password. Considering that early quantum computers will likely take quite long to solve even a single discrete logarithm, a quantum-annoying PAKE, combined with a large...

Protocols for password-based authenticated key exchange (PAKE) allow two users sharing only a short, low-entropy password to establish a secure session with a cryptographically strong key. The challenge in designing such protocols is that they must resist offline dictionary attacks in which an attacker exhaustively enumerates the dictionary of likely passwords in an attempt to match the used password. In this paper, we study the resilience of one particular PAKE against these attacks....

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,...

In response to standardization requests regarding password-authenticated key exchange (PAKE) protocols, the IRTF working group CFRG has setup a PAKE selection process in 2019, which led to the selection of the CPace protocol in the balanced setting, in which parties share a common password. In subsequent standardization efforts, the CPace protocol further developed, yielding a protocol family whose actual security guarantees in practical settings are not well understood. In this paper, we...

Cramer and Shoup introduced at Eurocrypt’02 the concept of hash proof system, also designated as smooth projective hash functions. Since then, they have found several applications, from building CCA-2 encryption as they were initially created for, to being at the core of several authenticated key exchange or even allowing witness encryption. In the post-quantum setting, the very few candidates use a language based on ciphertexts to build their hash proof system. This choice seems to...

The typical login protocol for authenticating a user to a web service involves the client sending a password over a TLS-secured channel to the service, occasionally deployed with the password being prehashed. This widely-deployed paradigm, while simple in nature, is prone to both inadvertent logging and eavesdropping attacks, and has repeatedly led to the exposure of passwords in plaintext. Partly to address this problem, symmetric and asymmetric PAKE protocols were developed to ensure that...

Symmetric password-authenticated key exchange (sPAKE) can be seen as an extension of traditional key exchange where two parties agree on a shared key if and only if they share a common secret (possibly low-entropy) password. We present the first sPAKE protocol to simultaneously achieve the following properties: - only two exponentiations per party, the same as plain unauthenticated Diffie-Hellman key agreement (and likely optimal); - optimal round complexity: a single flow (one message...

Password-Authenticated Key Exchange (PAKE) lets users with passwords exchange a cryptographic key. There have been two variants of PAKE which make it more applicable to real-world scenarios: - Asymmetric PAKE (aPAKE), which aims at protecting a client's password even if the authentication server is untrusted, and - Fuzzy PAKE (fPAKE), which enables key agreement even if passwords of users are noisy, but ``close enough''. Supporting fuzzy password matches eases the use of higher entropy...

It is standard practice that the secret key derived from an execution of a Password Authenticated Key Exchange (PAKE) protocol is used to authenticate and encrypt some data payload using a Symmetric Key Protocol (SKP). Unfortunately, most PAKEs of practical interest are studied using so-called game-based models, which – unlike simulation models – do not guarantee secure composition per se. However, Brzuska et al. (CCS 2011) have shown that middle ground is possible in the case of...

Recent advances in password-based authenticated key exchange (PAKE) protocols can offer stronger security guarantees for globally deployed security protocols. Notably, the OPAQUE protocol [Eurocrypt2018] realizes Strong Asymmetric PAKE (saPAKE), strengthening the protection offered by aPAKE to compromised servers: after compromising an saPAKE server, the adversary still has to perform a full brute-force search to recover any passwords or impersonate users. However, (s)aPAKEs do not protect...

Isogeny-based key establishment protocols are believed to be resistant to quantum cryptanalysis. Two such protocols---supersingular isogeny Diffie-Hellman (SIDH) and commutative supersingular isogeny Diffie-Hellman (CSIDH)---are of particular interest because of their extremely small public key sizes compared with other post-quantum candidates. Although SIDH and CSIDH allow us to achieve key establishment against passive adversaries and authenticated key establishment (using generic...

Protocols for password authenticated key exchange (PAKE) allow two parties who share only a weak password to agree on a cryptographically strong key. We revisit the notion of PAKE in the framework of universal composability, and propose a relaxation of the PAKE functionality of Canetti et al. that we call lazy-extraction PAKE (lePAKE). Roughly, our relaxation allows the ideal-world adversary to postpone its password guess even until after a session is complete. We argue that this relaxed...

We show that a slight variant of Protocol $\mathit{SPAKE2}+$, which was presented but not analyzed in Cash, Kiltz, and Shoup (2008) is a secure asymmetric password-authenticated key exchange protocol (PAKE), meaning that the protocol still provides good security guarantees even if a server is compromised and the password file stored on the server is leaked to an adversary. The analysis is done in the UC framework (i.e., a simulation-based security model), under the computational...

Password-based authenticated key exchange (PAKE) allows two parties with a shared password to agree on a session key. In the last decade, the design of PAKE protocols from lattice assumptions has attracted lots of attention. However, existing solutions in the standard model do not have appealing efficiency. In this work, we first introduce a new PAKE framework. We then provide two realizations in the standard model, under the Learning With Errors (LWE) and Ring-LWE assumptions,...

Non-repudiation of messages generated by users is a desirable feature in a number of applications ranging from online banking to IoT scenarios. However, it requires certified public keys and usually results in poor usability as a user must carry around his certificate (e.g., in a smart-card) or must install it in all of his devices. A user-friendly alternative, adopted by several companies and national administrations, is to have a ``cloud-based'' PKI. In a nutshell, each user has a PKI...

SPAKE2 is a balanced password-authenticated key exchange (PAKE) protocol, proposed by Abdalla and Pointcheval at CTRSA 2005. Due to its simplicity and efficiency, SPAKE2 is one of the balanced PAKE candidates currently under consideration for standardization by the CFRG, together with SPEKE, CPace, and J-PAKE. In this paper, we show that SPAKE2 achieves perfect forward security in the random-oracle model under the Gap Diffie-Hellman assumption. Unlike prior results, which either did not...

Password-Authenticated Key Exchange (PAKE) is a method to establish cryptographic keys between two users sharing a low-entropy password. In its asymmetric version, one of the users acts as a server and only stores some function of the password, e.g., a hash. Upon server compromise, the adversary learns H(pw). Depending on the strength of the password, the attacker now has to invest more or less work to reconstruct pw from H(pw). Intuitively, asymmetric PAKE seems more challenging than...

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 oine attacks. Asymmetric PAKE (aPAKE) [21] 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...

We introduce password-authenticated public-key encryption (PAPKE), a new cryptographic primitive. PAPKE enables secure end-to-end encryption between two entities without relying on a trusted third party or other out-of-band mechanisms for authentication. Instead, resistance to man-in-the-middle attacks is ensured in a human-friendly way by authenticating the public key with a shared password, while preventing offline dictionary attacks given the authenticated public key and/or the...

We consider the problem of constructing Diffie-Hellman (DH) parameters which pass standard approaches to parameter validation but for which the Discrete Logarithm Problem (DLP) is relatively easy to solve. We consider both the finite field setting and the elliptic curve setting. For finite fields, we show how to construct DH parameters $(p,q,g)$ for the safe prime setting in which $p=2q+1$ is prime, $q$ is relatively smooth but fools random-base Miller-Rabin primality testing with some...

Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure. We propose the first quantum-resistant password-authenticated key exchange scheme based on supersingular elliptic curve isogenies. The scheme is built upon supersingular isogeny Diffie-Hellman, and uses the password to generate permutations which obscure the...

Password managers (aka stores or vaults) allow a user to store and retrieve (usually high-entropy) passwords for her multiple password-protected services by interacting with a "device" serving the role of the manager (e.g., a smartphone or an online third-party service) on the basis of a single memorable (low-entropy) master password. Existing password managers work well to defeat offline dictionary attacks upon web service compromise, assuming the use of high-entropy passwords is enforced....

Increasingly connectivity becomes integrated in products and devices that previously operated in a stand-alone setting. This observation holds for many consumer ap- plications in the so-called "Internet of Things" (IoT) as well as for corresponding industry applications (IIoT), such as industrial process sensors. Often the only practicable means for authentication of human users is a password. The security of password-based authentication schemes frequently forms the weakest point of...

Password-Authenticated Key Exchange (PAKE) protocols allow two parties that only share a password to establish a shared key in a way that is immune to offline attacks. Asymmetric PAKE (aPAKE) strengthens this notion for the more common client-server setting where the server stores a mapping of the password and security is required even upon server compromise, that is, the only allowed attack in this case is an (inevitable) offline exhaustive dictionary attack against individual user...

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...

Secure Remote Password (SRP) protocol is an augmented Password-based Authenticated Key Exchange (PAKE) protocol based on discrete logarithm problem (DLP) with various attractive security features. Compared with basic PAKE protocols, SRP does not require server to store user's password and user does not send password to server to authenticate. These features are desirable for secure client-server applications. SRP has gained extensive real-world deployment, including Apple iCloud, 1Password...

Two post-quantum password-based authenticated key exchange (PAKE) protocols were proposed at CT-RSA 2017. Following this work, we give much more efficient and portable C++ implementation of these two protocols. We also choose more compact parameters providing 200-bit security. Compared with original implementation, we achieve 21.5x and 18.5x speedup for RLWE-PAK and RLWE-PPK respectively. Compare with quantum-vulnerable J-PAKE protocol, we achieve nearly 8x speedup. We also integrate...

Consider key agreement by two parties who start out knowing a common secret (which we refer to as “pass-string”, a generalization of “password”), but face two complications: (1) the pass-string may come from a low-entropy distribution, and (2) the two parties’ copies of the pass-string may have some noise, and thus not match exactly. We provide the first efficient and general solutions to this problem that enable, for example, key agreement based on commonly used biometrics such as iris...

We present a security reduction for the PAK protocol instantiated over Gap Diffie-Hellman Groups that is tighter than previously known reductions. We discuss the implications of our results for concrete security. Our proof is the first to show that the PAK protocol can provide meaningful security guarantees for values of the parameters typical in today's world.

Password Authenticated Key Exchange (PAKE) allows a user to establish a strong cryptographic key with a server, using only knowledge of a pre-shared password. One of the basic security requirements of PAKE is to prevent offline dictionary attacks. In this paper, we revisit zkPAKE, an augmented PAKE that has been recently proposed by Mochetti, Resende, and Aranha (SBSeg 2015). Our work shows that the zkPAKE protocol is prone to offline password guessing attack, even in the presence of an...

Password-based authenticated key exchange (PAKE) enables two users with shared low-entropy passwords to establish cryptographically strong session keys over insecure networks. At Asiacrypt 2009, Katz and Vaikuntanathan showed a generic three-round PAKE based on any CCA-secure PKE with associated approximate smooth projective hashing (ASPH), which helps to obtain the first PAKE from lattices. In this paper, we give a framework for constructing PAKE from CCA-secure PKE with associated ASPH,...

Connectivity becomes increasingly important also for small embedded systems such as typically found in industrial control installations. More and more use-cases require secure remote user access increasingly incorporating handheld based human machine interfaces, using wireless links such as Bluetooth. Correspondingly secure operator authentication becomes of utmost importance. Unfortunately, often passwords with all their well-known pitfalls remain the only practical mechanism. We present an...

We propose the first user authentication and key exchange protocols that can tolerate strong corruptions on the client-side. If a user happens to log in to a server from a terminal that has been fully compromised, then the other past and future user's sessions initiated from honest terminals stay secure. We define the security model for Human Authenticated Key Exchange (HAKE) protocols and first propose two generic protocols based on human-compatible (HC) function family,...

Password-based Authenticated Key-Exchange (PAKE) protocols allow users, who need only to share a password, to compute a high-entropy shared session key despite passwords being taken from a dictionary. Security models for PAKE protocols aim to capture the desired security properties that such protocols must satisfy when executed in the presence of an active adversary. They are usually classified into i) indistinguishability-based (IND-based) or ii) simulation-based (SIM-based). The relation...

We present TOPPSS, the most efficient Password-Protected Secret Sharing (PPSS) scheme to date. A (t; n)-threshold PPSS, introduced by Bagherzandi et al, allows a user to share a secret among n servers so that the secret can later be reconstructed by the user from any subset of t+1 servers with the sole knowledge of a password. It is guaranteed that any coalition of up to t corrupt servers learns nothing about the secret (or the password). In addition to providing strong protection to secrets...

Three-party Password Authenticated Key Exchange (3PAKE) protocol is an important cryptographic primitive, where clients can establish a session key using easy-to-remember passwords. A number of 3PAKE protocols based on traditional mathematical problems have been presented in the literature, but these protocols are not able to resist attacks using quantum computers. In this paper, we construct the first 3PAKE protocol from lattices. Lattice-based cryptography is a promising post-quantum...

We show how to build a UC-Secure Oblivious Transfer in the presence of Adaptive Corruptions from Quasi-Adaptive Non-Interactive Zero-Knowledge proofs. Our result is based on the work of Jutla and Roy at Asiacrypt 2015, where the authors proposed a constant-size very efficient PAKE scheme. As a stepping stone, we first show how a two-flow PAKE scheme can be generically transformed in an optimized way, in order to achieve an efficient three-flow Oblivious-Transfer scheme. We then compare our...

Group Password-Based Authenticated Key Exchange (GPAKE) allows a group of users to establish a secret key, as long as all of them share the same password. However, in existing GPAKE protocols as soon as one user runs the protocol with a non-matching password, all the others abort and no key is established. In this paper we seek for a more flexible, yet secure, GPAKE and put forward the notion of partitioned GPAKE. Partitioned GPAKE tolerates users that run the protocol on different...

Authenticated Key Exchange (AKE) is a cryptographic scheme with the aim to establish a high-entropy and secret session key over a insecure communications network. \emph{Password}-Authenticated Key Exchange (PAKE) assumes that the parties in play share a simple password, which is cheap and human-memorable and is used to achieve the authentication. PAKEs are practically relevant as these features are extremely appealing in an age where most people access sensitive personal data remotely...

Two-Server Password Authenticated Key Exchange (2PAKE) protocols apply secret sharing techniques to achieve protection against server-compromise attacks. 2PAKE protocols eliminate the need for password hashing and remain secure as long as one of the servers remains honest. This concept has also been explored in connection with two-server password authenticated secret sharing (2PASS) protocols for which game-based and universally composable versions have been proposed. In contrast,...

We propose Blind Password Registration (BPR), a new class of cryptographic protocols that is instrumental for secure registration of client passwords at remote servers with additional protection against unwitting password disclosures on the server side that may occur due to the lack of the state-of-the-art password protection mechanisms implemented by the server or due to common server-compromise attacks. The dictionary attack resistance property of BPR protocols guarantees that the only...

Recently, the password-authenticated key exchange protocol J-PAKE of Hao and Ryan (Workshop on Security Protocols 2008) was formally proven secure in the algebraic adversary model by Abdalla et al.(IEEE S&P 2015). In this paper, we propose and examine two variants of J-PAKE - which we call RO-J-PAKE and CRS-J-PAKE - that each makes the use of two less zero-knowledge proofs than the original protocol. We show that they are provably secure following a similar strategy to that of Abdalla et al....

Smooth projective hashing has proven to be an extremely useful primitive, in particular when used in conjunction with commitments to provide implicit decommitment. This has lead to applications proven secure in the UC framework, even in presence of an adversary which can do adaptive corruptions, like for example Password Authenticated Key Exchange (PAKE), and 1-out-of-m Oblivious Transfer (OT). However such solutions still lack in efficiency, since they heavily scale on the underlying...

We introduce a novel notion of smooth (-verifier) non-interactive zero-knowledge proofs (NIZK) which parallels the familiar notion of smooth projective hash functions (SPHF). We also show that the recent single group element quasi-adaptive NIZK (QA-NIZK) of Jutla and Roy (CRYPTO 2014) for linear subspaces can be easily extended to be computationally smooth. One important distinction of the new notion from SPHFs is that in a smooth NIZK the public evaluation of the hash on a language...

PPSS is a central primitive introduced by Bagherzandi et al [BJSL10] which allows a user to store a secret among n servers such that the user can later reconstruct the secret with the sole possession of a single password by contacting t+1 servers for t<n. At the same time, an attacker breaking into t of these servers - and controlling all communication channels - learns nothing about the secret (or the password). Thus, PPSS schemes are ideal for on-line storing of valuable secrets when...

In this paper the Security Evaluated Standardized Password Authenticated Key Exchange (SESPAKE) protocol is proposed (this protocol is approved in the standardization system of the Russian Federation) and its cryptographic properties are analyzed. The SESPAKE protocol includes a key agreement step and a key authentication step. We define new indistinguishability-based adversary model with a threat of false authentication that is an extension of the original indistinguishability-based model...

We introduce a setting that we call Device-Enhanced PAKE (DE-PAKE), where PAKE (password-authenticated key exchange) protocols are strengthened against online and offline attacks through the use of an auxiliary device that aids the user in the authentication process. We build such schemes and show that their security, properly formalized, achieves maximal-attainable resistance to online and offline attacks in both PKI and PKI-free settings. In particular, an online attacker must guess the...

In this paper, we propose an efficient identity-based password authenticated key exchange (IBPAKE) protocol using identity-based KEM/DEM. In IBPAKE, a client conducts authentication based on a human-memorable password and a server's identity. A distinctive feature of IBPAKE protocols, compared to the well-known EKE-type PAKE protocols, is that an adversary who even acquired a user's password cannot impersonate a server to further investigate user's sensitive information. We first construct...

The multiple ideal query (MIQ) model [Goyal, Jain, and Ostrovsky, Crypto'10] offers a relaxed notion of security for concurrent secure computation, where the simulator is allowed to query the ideal functionality multiple times per session (as opposed to just once in the standard definition). The model provides a quantitative measure for the degradation in security under concurrent self-composition, where the degradation is measured by the number of ideal queries. However, to date, all...

Encrypting data on client-side before uploading it to a cloud storage is essential for protecting users' privacy. However client-side encryption is at odds with the standard practice of deduplication. Reconciling client-side encryption with cross-user deduplication is an active research topic. We present the first secure cross-user deduplication scheme that supports client-side encryption {\em without requiring any additional independent servers}. Interestingly, the scheme is based on...

Password-authenticated key exchange (PAKE) protocols allow two players to agree on a shared high entropy secret key, that depends on their own passwords only. Following the Gennaro and Lindell's approach, with a new kind of smooth-projective hash functions (SPHFs), Katz and Vaikuntanathan recently came up with the first concrete one-round PAKE protocols, where the two players just have to send simultaneous flows to each other. The first one is secure in the Bellare-Pointcheval-Rogaway (BPR)...

In this paper, we study Password Authenticated Key Exchange (PAKE) in a group. First, we present a generic ``fairy-ring dance'' construction that transforms any secure two-party PAKE scheme to a group PAKE protocol while preserving the round efficiency in the optimal way. Based on this generic construction, we present two concrete instantiations based on using SPEKE and J-PAKE as the underlying PAKE primitives respectively. The first protocol, called SPEKE+, accomplishes authenticated key...

We introduce a novel concept of dual-system simulation-sound non-interactive zero-knowledge (NIZK) proofs. Dual-system NIZK proof system can be seen as a two-tier proof system. As opposed to the usual notion of zero-knowledge proofs, dual-system defines an intermediate partial-simulation world, where the proof simulator may have access to additional auxiliary information about the potential language member, for example a membership bit, and simulation of proofs is only guaranteed if the...

In a Password-Protected Secret Sharing (PPSS) scheme with parameters (t,n) (formalized by Bagherzandi et al), a user Alice stores secret information s among n servers so that she can later recover the information solely on the basis of her password. The security requirement is similar to a (t,n)-threshold secret sharing, i.e., Alice can recover her secret as long as she can communicate with t + 1 honest servers but an attacker gaining access to t servers cannot learn information about the...

Indistinguishability under chosen-ciphertext attack (INDCCA) is now considered the de facto security notion for public-key encryption. However, this sometimes offers a stronger security guarantee than what is needed. In this paper, we consider a weaker security notion, termed indistinguishability under plaintext-checking attacks (INDPCA), in which the adversary has only access to an oracle indicating whether or not a given ciphertext encrypts a given message. After formalizing this notion,...

The SPEKE protocol is commonly considered one of the classic Password Authenticated Key Exchange (PAKE) schemes. It has been included in international standards (particularly, ISO/IEC 11770-4 and IEEE 1363.2) and deployed in commercial products (e.g., Blackberry). We observe that the original SPEKE specification is subtly different from those defined in the ISO/IEC 11770-4 and IEEE 1363.2 standards. We show that those differences have critical security implications by presenting two new...

Smooth projective hash functions have been used as building block for various cryptographic applications, in particular for password-based authentication. In this work we propose the extended concept of distributed smooth projective hash functions where the computation of the hash value is distributed across $n$ parties and show how to instantiate the underlying approach for languages consisting of Cramer-Shoup ciphertexts. As an application of distributed smooth projective hashing we...

A threshold password-authenticated key exchange (T-PAKE) protocol allows a set of n servers to collectively authenticate a client with a human-memorizable password such that any subset of size greater than a threshold t can authenticate the client, while smaller subsets of servers learn no information about the password. With its protection against offline dictionary attacks, T-PAKE provides a practical solution for an important real-life problem with password authentication. However, the...

Zero-Knowledge Password Policy Checks (ZKPPC), introduced in this work, enable blind registration of client passwords at remote servers, i.e., client passwords are never transmitted to the servers. This eliminates the need for trusting servers to securely process and store client passwords. A ZKPPC protocol, executed as part of the registration procedure, allows clients to further prove compliance of chosen passwords with respect to password policies defined by the servers. The main...

An important problem in secure multi-party computation is the design of protocols that can tolerate adversaries that are capable of corrupting parties dynamically and learning their internal states. In this paper, we make significant progress in this area in the context of password-authenticated key exchange (PAKE) and oblivious transfer (OT) protocols. More precisely, we first revisit the notion of projective hash proofs and introduce a new feature that allows us to \emph{explain} any...

We present the first provably-secure 3-party password-only authenticated key exchange (PAKE) protocol that can run in only two communication rounds. Our protocol is generic in the sense that it can be constructed from any 2-party PAKE protocol. The protocol is proven secure in a variant of the widely accepted model of Bellare, Pointcheval and Rogaway (2000) without any idealized assumptions on the cryptographic primitives used. We also investigate the security of the 2-round 3-party PAKE...

While password-authenticated key exchange (or PAKE) protocols have been deeply studied, a server corruption remains the main threat, with many concrete cases nowadays. Verifier-based PAKE (or VPAKE) protocols, initially called Augmented-PAKE, have been proposed to limit the impact of any leakage. However, no satisfactory security model has ever been proposed to quantify the actual security of a protocol in the standard model. The unique model proposed so far is an ideal functionality in the...

Smooth Projective Hash Functions are one of the base tools to build interactive protocols; and this notion has lead to the construction of numerous protocols enjoying strong security notions, such as the security in the Bellare-Pointcheval-Rogaway (BPR) model or even Universal Composability (UC). Yet, the construction of SPHF has been almost limited to discrete-logarithm or pairing type assumptions up to now. This stands in contrast with domains such as homomorphic encryption or functional...

Despite all the research efforts made so far, the design of protocols for password-authenticated key exchange (PAKE) still remains a non-trivial task. One of the major challenges in designing such protocols is to protect low-entropy passwords from the notorious dictionary attacks. In this work, we revisit Abdalla and Pointcheval's three-party PAKE protocol presented in Financial Cryptography 2005, and demonstrate that the protocol is vulnerable to an off-line dictionary attack whereby a...

In 2009, Abdalla et al. proposed a reasonably practical password-authenticated key exchange (PAKE) secure against adaptive adversaries in the universal composability (UC) framework. It exploited the Canetti-Fischlin methodology for commitments and the Cramer-Shoup smooth projective hash functions (SPHFs), following the Gennaro-Lindell approach for PAKE. In this paper, we revisit the notion of non-interactive commitments, with a new formalism that implies UC security. In addition, we provide...

Katz and Vaikuntanathan recently improved smooth projective hash functions in order to build one-round password-authenticated key exchange protocols (PAKE). To achieve security in the UC framework they allowed the simulator to extract the hashing key, which required simulation-sound non-interactive zero-knowledge proofs that are unfortunately inefficient. We improve the way the latter extractability is obtained by introducing the notion of trapdoor smooth projective hash function (TSPHF). A...

In this work we introduce the notion of Oblivious Password based Authenticated Key Exchange (O-PAKE) and a compiler to transform a large class of PAKE into O-PAKE protocols. O-PAKE allows a client that shares one password with a server to use a set of passwords within one PAKE session. It succeeds if and only if one of those input passwords matches the one stored on the server side. The term oblivious is used to emphasise that no information about any password, input by the client, is made...