Strong asymmetric password-authenticated key exchange (saPAKE) is the gold standard for password-based authentication. When authenticating using saPAKE, the client holds a cleartext password, and the server holds only a "digest" of the password. The two parties obtain a shared session key if and only if the client password matches the password encoded in the digest. In this work we initiate the study of strong asymmetric fuzzy PAKE (safPAKE), which allows the client and server to...

Symmetric encryption allows us to establish a secure channel based on a shared, strong key. However, users cannot remember or cannot store such keys securely. Password-Authenticated Key Exchange (PAKE) protocols address this by using low-entropy, human-memorizable passwords to establish secure channels. PAKEs are widely used and are foundational in practical cryptographic protocols, but while cryptographic tools like Key Encapsulation Mechanism (KEM) and Signatures have been implemented to...

Authenticated Key Exchange (AKE) between any two entities is one of the most important security protocols available for securing our digital networks and infrastructures. In PQCrypto 2023, Bruckner, Ramacher and Striecks proposed a novel hybrid AKE (HAKE) protocol dubbed Muckle+ that is particularly useful in large quantum-safe networks consisting of a large number of nodes. Their protocol is hybrid in the sense that it allows key material from conventional, post-quantum, and quantum...

We present a highly efficient authenticated group key exchange protocol, TEAKEX, using only symmetric key primitives. Our protocol provides proven strong security, including forward secrecy, post-compromise security, and post-quantum security. For online applications we claim that TEAKEX is much simpler and more efficient than currently available alternatives. As part of our construction we also give a new abstract security definition for delayed authentication and describe its instantiation...

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to jointly establish a cryptographic key, where the only information shared in advance is a low-entropy password. The first efficient PAKE protocol whose security does not rely on the random oracle model is the one by Katz, Ostrovsky and Yung (KOY, EUROCRYPT 2001). Unfortunately, the KOY protocol has only been proven secure in the game-based setting, and it is unclear whether KOY is secure in the stronger Universal...

Symmetric-key authenticated key establishment (AKE) protocols are particularly well suited in resource constraint environments such as internet of things (IoT) devices. Moreover, they often rely on better understood assumptions than asymmetric ones. In this paper, we review the security model for symmetric-key AKE protocols. We show why several existing models allow trivial attacks while they do not protect against some non-trivial ones. We fix these issues with our new security...

A conventional Authenticated Key Exchange (AKE) protocol consumes fresh random coins from the local random source. However, recent studies of bad randomness expose the vulnerability of some AKE protocols under small subgroup attacks when the random coins are manipulated or being repeated. It is important to ensure the bad randomness of one random source will not affect the security of the AKE protocol as a whole. Thus, we introduce the notion of remote randomness by introducing...

Passports, identity cards and travel visas are examples of machine readable travel documents (MRTDs) or eMRTDs for their electronic variants. The security of the data exchanged between these documents and a reader is secured with a standardized password authenticated key exchange (PAKE) protocol known as PACE. A new world-wide protocol migration is expected with the arrival of post-quantum cryptography (PQC) standards. In this paper, we focus on the impact of this migration on constrained...

Let us assume that one of two trusted parties (administrator) manages the information system (IS) and another one (user) is going to use the resources of this IS during the certain time interval. So they need establish secure user’s access password to the IS resources of this system via selected authenticated key exchange protocol. So they need to communicate via insecure communication channel and secretly con-struct a cryptographically strong session key that can serve for the...

Let us assume that one of two trusted parties (administrator) manages the information system (IS) and another one (user) is going to use the resources of this IS during the certain time interval. So they need establish secure user’s access password to the IS resources of this system via selected authenticated key exchange protocol. So they need to communicate via insecure communication channel and secretly con-struct a cryptographically strong session key that can serve for the...

The Secure Shell (SSH) protocol is one of the first security protocols on the Internet to upgrade itself to resist attacks against future quantum computers, with the default adoption of the "quantum (otherwise, classically)" secure hybrid key exchange in OpenSSH from April 2022. However, there is a lack of a comprehensive security analysis of this quantum-resistant version of SSH in the literature: related works either focus on the hybrid key exchange in isolation and do not consider...

We consider adversaries able to perform a nonzero but small number of discrete logarithm computations, as would be expected with near-term quantum computers. Schemes with public parameters consisting of a few group elements are now at risk; could an adversary knowing the discrete logarithms of these elements go on to easily compromise the security of many users? We study this question for known schemes and find, across them, a perhaps surprising variance in the answers. In a first class are...

Password-Authenticated Key Exchange (PAKE) establishes a secure channel between two parties who share a password. Asymmetric PAKE is a variant of PAKE, where one party stores a hash of the password to preserve security under the situation that the party is compromised. The security of PAKE and asymmetric PAKE is often analyzed in the framework of universal composability (UC). Abdalla et al. (CRYPTO '20) relaxed the UC security of PAKE and showed that the relaxed security still guarantees...

Deniable authentication allows Alice to authenticate a message to Bob, while retaining deniability towards third parties. In particular, not even Bob can convince a third party that Alice authenticated that message. Clearly, in this setting Bob should not be considered trustworthy. Furthermore, deniable authentication is necessary for deniable key exchange, as explicitly desired by Signal and off-the-record (OTR) messaging. In this work we focus on (publicly verifiable) designated...

In this work we revisit the post-quantum security of KEM-based password-authenticated key exchange (PAKE), specifically that of (O)CAKE. So far, these schemes evaded a security proof considering quantum adversaries. We give a detailed analysis of why this is the case, determining the missing proof techniques. To this end, we first provide a proof of security in the post-quantum setting, up to a single gap. This proof already turns out to be technically involved, requiring advanced techniques...

Hiding the metadata in Internet protocols serves to protect user privacy, dissuade traffic analysis, and prevent network ossification. Fully encrypted protocols require even the initial key exchange to be obfuscated: a passive observer should be unable to distinguish a protocol execution from an exchange of random bitstrings. Deployed obfuscated key exchanges such as Tor's pluggable transport protocol obfs4 are Diffie–Hellman-based, and rely on the Elligator encoding for obfuscation....

This paper examines whether a revocation function can be added to a protocol, protocol FSU, which is an asymmetric pairing variant of a protocol that has been adopted as an international standard, ISO/IEC11770-3. Protocol FSU is an identity-based authenticated-key exchange protocol based on a mathematical problem, an asymmetric gap bilinear Diffie--Hellman (GBDH) problem. To make protocol FSU revocable, a generic technique is applied, which converts an identity-based encryption scheme to a...

Password-Authenticated Key Exchange (PAKE) is a type of key exchange protocols secure against man-in-the-middle adversaries, in the setting where the two parties only agree upon a low-entropy "password" in advance. The first and arguably most well-studied PAKE protocol is Encrypted Key Exchange (EKE) (Bellovin and Marritt, 1992), and the standard security notion for PAKE is in the Universal Composability (UC) framework (Canetti et al., 2005). While the UC-security of EKE has been "folklore"...

We show a generic compiler from KEM to (Universally Composable) PAKE in the Random Oracle Model (ROM) and without requiring an Ideal Cipher. The compiler is akin to Encrypted Key Exchange (EKE) by Bellovin-Merritt, but following the work of McQuoid et al. it uses only a 2-round Feistel to password-encrypt a KEM public key. The resulting PAKE incurs only insignificant cost overhead over the underlying KEM, and it is a secure UC PAKE if KEM is secure and key-anonymous under the...

Password Authenticated Key Exchange (PAKE) establishes secure communication channels using relatively short, often human memorable, passwords for authentication. The currently standardized PAKEs however rely on classical asymmetric (public key) cryptography. Thus, these classical PAKEs may become insecure, should the expected quantum threat become a reality. Despite the growing interest in realizing quantum-safe PAKEs, they did not receive much attention from the ongoing Post-Quantum...

The Signal protocol relies on a special handshake protocol, formerly X3DH and now PQXDH, to set up secure conversations. Prior analyses of these protocols (or proposals for post-quantum alternatives) have all used highly tailored models to the individual protocols and generally made ad-hoc adaptations to "standard" AKE definitions, making the concrete security attained unclear and hard to compare between similar protocols. Indeed, we observe that some natural Signal handshake protocols...

We present the No IC Encryption (NICE)-PAKE, a (semi)-generic symmetric Password Authenticated Key Exchange (PAKE) framework providing a quantum-safe alternative for the Ideal Cipher (IC), utilizing simpler cryptographic components for the authentication step. To give a formal proof, we introduce the notions of A-Part Secrecy (A-SEC-CCA), Splittable Collision Freeness (A-CFR-CCA) and Public Key Uniformity (SPLIT-PKU) for splittable LWE KEMs. We show the relation of the former to the...

In this work, we present a new paradigm for constructing Group Authenticated Key Exchange (GAKE). This result is the first tightly secure GAKE scheme in a strong security model that allows maximum exposure attacks (MEX) where the attacker is allowed to either reveal the secret session state or the long-term secret of all communication partners. Moreover, our protocol features the strong and realistic notion of (full) perfect forward secrecy (PFS), that allows the attacker to actively modify...

For Password-Based Authenticated Key Exchange (PAKE), an idealized setup such as random oracle (RO) or a trusted setup such as common reference string (CRS) is a must in the universal composability (UC) framework (Canetti, FOCS 2001). Given the potential failure of a CRS or RO setup, it is natural to consider distributing trust among the two setups, resulting a CRS-or-RO-setup (i.e., CoR-setup). However, the infeasibility highlighted by Katz et al. (PODC 2014) suggested that it is...

A hybrid cryptosystem combines two systems that fulfill the same cryptographic functionality, and its security enjoys the security of the harder one. There are many proposals for hybrid public-key encryption (hybrid PKE), hybrid signature (hybrid SIG) and hybrid authenticated key exchange (hybrid AKE). In this paper, we fill the blank of Hybrid Password Authentication Key Exchange (hybrid PAKE). For constructing hybrid PAKE, we first define an important class of PAKE -- full DH-type...

Much work has been done recently on developing password-authenticated key exchange (PAKE) mechanisms with post-quantum security. However, modern guidance recommends the use of hybrid schemes—schemes which rely on the combined hardness of a post-quantum assumption, e.g., Learning with Errors (LWE), and a more traditional assumption, e.g., decisional Diffie-Hellman. To date, there is no known hybrid PAKE construction, let alone a general method for achieving such. In this paper, we present...

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 the case all servers are compromised, 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 [JKX18], where the server stores a password...

Anamorphic encryptions and anamorphic signatures assume a double key pre-shared between two parties so as to enable the transmission of covert messages. How to securely and efficiently distribute a double key under the dictator's surveillance is a central problem for anamorphic cryptography, especially when the users are forced to surrender their long-term secret keys or even the randomness used in the algorithms to the dictator. In this paper, we propose Anamorphic Authentication Key...

Password Authenticated Key Exchange (PAKE) allows two parties to establish a secure session key with a shared low-entropy password pw. Asymmetric PAKE (aPAKE) extends PAKE in the client-server setting, and the server only stores a password file instead of the plain password so as to provide additional security guarantee when the server is compromised. In this paper, we propose a novel generic compiler from PAKE to aPAKE in the Universal Composable (UC) framework by making use of Key...

Passwords are widely adopted for user authentication in practice, which led to the question of whether we can bootstrap a strongly-secure setting based on them. Historically, this has been extensively studied for key exchange; bootstrap from a low-entropy password to a high entropy key securing the communication. Other instances include digital lockers, signatures, secret sharing, and encryption. Motivated by a recent work on consumable tokens (Almashaqbeh et al., Eurocrypt 2022), we...

In the multi-user with corruptions (muc) setting there are $n\geq 1$ users, and the goal is to prove that, even in the face of an adversary that adaptively corrupts users to expose their keys, un-corrupted users retain security. This can be considered for many primitives including signatures and encryption. Proofs of muc security, while possible, generally suffer a factor n loss in tightness, which can be large. This paper gives new proofs where this factor is reduced to the number c of...

Transitioning from classically to quantum secure key agreement protocols may require to exchange fundamental components, for example, exchanging Diffie-Hellman-like key exchange with a key encapsulation mechanism (KEM). Accordingly, the corresponding security proof can no longer rely on the Diffie-Hellman assumption, thus invalidating the security guarantees. As a consequence, the security properties have to be re-proven under a KEM-based security notion. We initiate the study of the...

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...

Ring signatures, a cryptographic primitive introduced by Rivest, Shamir and Tauman (ASIACRYPT 2001), offer signer anonymity within dynamically formed user groups. Recent advancements have focused on lattice-based constructions to improve efficiency, particularly for large signing rings. However, current state-of-the-art solutions suffer from significant overhead, especially for smaller rings. In this work, we present a novel NTRU-based ring signature scheme, Gandalf, tailored towards...

Asymmetric Password-Authenticated Key Exchange (aPAKE) protocols, particularly Strong aPAKE (saPAKE) have enjoyed significant attention, both from academia and industry, with the well-known OPAQUE protocol currently undergoing standardization. In (s)aPAKE, a client and a server collaboratively establish a high-entropy key, relying on a previously exchanged password for authentication. A main feature is its resilience against offline and precomputation (for saPAKE) attacks. OPAQUE, as well as...

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...

Physically Unclonable Functions (PUFs) have been a potent choice for enabling low-cost, secure communication. However, in most applications, one party holds the PUF, and the other securely stores the challenge-response pairs (CRPs). It does not remove the need for secure storage entirely, which is one of the goals of PUFs. This paper proposes a PUF-based construction called Harmonizing PUFs ($\textsf{H_PUF}$s), allowing two independent PUFs to generate the same outcome without storing...

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...

Weak forward secrecy (wFS) of authenticated key exchange (AKE) protocols is a passive variant of (full) forward secrecy (FS). A natural mechanism to upgrade from wFS to FS is the use of key confirmation messages which compute a message authentication code (MAC) over the transcript. Unfortunately, Gellert, Gjøsteen, Jacobson and Jager (GGJJ, CRYPTO 2023) show that this mechanism inherently incurs a loss proportional to the number of users, leading to an overall non-tight reduction, even if...

The iMessage PQ3 protocol is an end-to-end encrypted messaging protocol designed for exchanging data in long-lived sessions between two devices. It aims to provide classical and post-quantum confidentiality for forward secrecy and post-compromise secrecy, as well as classical authentication. Its initial authenticated key exchange is constructed from digital signatures plus elliptic curve Diffie–Hellman and post-quantum key exchanges; to derive per-message keys on an ongoing basis, it employs...

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 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...

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...

In 2016, NIST announced an open competition with the goal of finding and standardizing a suitable quantum-resistant cryptographic algorithm, with the standard to be drafted in 2023. These algorithms aim to implement post-quantum secure key encapsulation mechanism (KEM) and digital signatures. However, the proposed algorithm does not consider authentication and is vulnerable to attacks such as man-in-the-middle. In this paper, we propose an authenticated key exchange algorithm to solve the...

The rapid digitization of aviation communication and its dependent critical operations demand secure protocols that address domain-specific security requirements within the unique functional constraints of the aviation industry. These secure protocols must provide sufficient security against current and possible future attackers, given the inherent nature of the aviation community, that is highly complex and averse to frequent upgrades as well as its high safety and cost considerations. In...

Universal thresholdizer (UT) was proposed by Boneh et al. in CRYPTO'18 as a general framework for thresholdizing non-threshold cryptographic primitives where a set of $N$ servers, each gets a share such that any set of $k$ servers, each produces a partial result, which can be combined to generate the final result. In many applications of threshold cryptography such as the protection of private keys in a digital wallet, the combining operation of partial results must be protected. In this...

In this paper, we study the design of efficient signature and public-key encryption (PKE) schemes in the presence of both leakage and tampering attacks. Firstly, we formalize the strong leakage and tamper-resilient (sLTR) security model for signature, which provides strong existential unforgeability, and deals with bounded leakage and restricted tampering attacks, as a counterpart to the sLTR security introduced by Sun et al. (ACNS 2019) for PKE. Then, we present direct constructions...

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...

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...

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 give a tighter security proof for authenticated key exchange (AKE) protocols that are generically constructed from key encapsulation mechanisms (KEMs) in the quantum random oracle model (QROM). Previous works (Hövelmanns et al., PKC 2020) gave reductions for such a KEM-based AKE protocol in the QROM to the underlying primitives with square-root loss and a security loss in the number of users and total sessions. Our proof is much tighter and does not have square-root loss. Namely, it only...

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 $k_H$...

Public data can be authenticated by obtaining from a trustworthy website with TLS. Private data, such as user profile, are usually restricted from public access. If a user wants to authenticate his private data (e.g., address) provided by a restricted website (e.g., user profile page of a utility company website) to a verifier, he cannot simply give his username and password to the verifier. DECO (CCS 2020) provides a solution for liberating these data without introducing undesirable trust...

This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of ``generic algorithms''---that is, algorithms that do not exploit any properties of the group encoding. We establish the quantum generic group model and hybrid classical-quantum generic group model as quantum and hybrid analogs of their classical counterpart. This model counts the number of group operations of the underlying cyclic group $G$ as a...

WhatsApp is an end-to-end encrypted (E2EE) messaging service used by billions of people. In late 2021, WhatsApp rolled out a new protocol for backing up chat histories. The E2EE WhatsApp backup protocol (WBP) allows users to recover their chat history from passwords, leaving WhatsApp oblivious of the actual encryption keys. The WBP builds upon the OPAQUE framework for password-based key exchange, which is currently undergoing standardization. While considerable efforts have gone into the...

We construct the first tightly secure authenticated key exchange (AKE) protocol from lattices. Known tight constructions are all based on Diffie-Hellman-like assumptions. Thus, our protocol is the first construction with tight security from a post-quantum assumption. Our AKE protocol is constructed tightly from a new security notion for key encapsulation mechanisms (KEMs), called one-way security against checkable chosen-ciphertext attacks (OW- ChCCA). We show how an OW-ChCCA secure KEM...

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...

In this work, we set out to create a subversion resilient authenticated key exchange protocol. The first step was to design a meaningful security model for this primitive, and our goal was to avoid using building blocks like reverse firewalls and public watchdogs. We wanted to exclude these kinds of tools because we desired that our protocols to be self contained in the sense that we could prove security without relying on some outside, tamper-proof party. To define the model, we began by...

In two-message authenticated key exchange (AKE), it is necessary for the initiator to keep a round state after sending the first round-message, because he/she has to derive his/her session key after receiving the second round-message. Up to now almost all two-message AKEs constructed from public-key encryption (PKE) only achieve weak security which does not allow the adversary obtaining the round state. How to support state reveal to obtain a better security called IND-AA security has been...

End-to-end authenticity in public networks plays a significant role. Namely, without authenticity, the adversary might be able to retrieve even confidential information straight away by impersonating others. Proposed solutions to establish an authenticated channel cover pre-shared key-based, password-based, and certificate-based techniques. To add confidentiality to an authenticated channel, authenticated key exchange (AKE) protocols usually have one of the three solutions built in. As an...

We show how to embed a covert key exchange sub protocol within a regular TLS 1.3 execution, generating a stealth key in addition to the regular session keys. The idea, which has appeared in the literature before, is to use the exchanged nonces to transport another key value. Our contribution is to give a rigorous model and analysis of the security of such embedded key exchanges, requiring that the stealth key remains secure even if the regular key is under adversarial control. Specifically...

Oblivious Pseudorandom Functions (OPRFs) are an elementary building block in cryptographic and privacy-preserving applications. However, while there are numerous pre-quantum secure OPRF constructions, few options exist in a post-quantum secure setting, and of those even fewer are practical for modern-day applications. In this work, we focus on isogeny group actions, as the associated low bandwidth leads to efficient constructions. Our results focus on the Naor-Reingold OPRF. We introduce...

Quantum key distribution (QKD) allows Alice and Bob to agree on a shared secret key, while communicating over a public (untrusted) quantum channel. Compared to classical key exchange, it has two main advantages: (i) The key is unconditionally hidden to the eyes of any attacker, and (ii) its security assumes only the existence of authenticated classical channels which, in practice, can be realized using Minicrypt assumptions, such as the existence of digital signatures. On the flip side, QKD...

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...

We introduce the notion of a quantum trapdoor function. This is an efficiently computable unitary that takes as input a "public" quantum state and a classical string $x$, and outputs a quantum state. This map is such that (i) it is hard to invert, in the sense that it is hard to recover $x$ given the output state (and many copies of the public state), and (ii) there is a classical trapdoor that allows efficient inversion. We show that a quantum trapdoor function can be constructed from any...

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...

We define the Generic Group Action Model (GGAM), an adaptation of the Generic Group Model to the setting of group actions (such as CSIDH). Compared to a previously proposed definition by Montgomery and Zhandry (ASIACRYPT'22), our GGAM more accurately abstracts the security properties of group actions. We are able to prove information-theoretic lower bounds in the GGAM for the discrete logarithm assumption, as well as for non-standard assumptions recently introduced in the setting of...

(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...

A key encapsulation mechanism (KEM) is a basic building block for key exchange which must be combined with long-term keys in order to achieve authenticated key exchange (AKE). Although several KEM-based AKE protocols have been proposed, KEM-based modular building blocks are not available. We provide a KEM-based authenticator and a KEM-based protocol in the Authenticated Links model (AM), in the terminology of Canetti and Krawczyk (2001). Using these building blocks we achieve a set of...

We introduce CorrGapCDH, the Gap Computational Diffie-Hellman problem in the multi-user setting with Corruptions. In the random oracle model, our assumption tightly implies the security of the authenticated key exchange protocols NAXOS in the eCK model and (a simplified version of) X3DH without ephemeral key reveal. We prove hardness of CorrGapCDH in the generic group model, with optimal bounds matching the one of the discrete logarithm problem. We also introduce CorrCRGapCDH, a stronger...

EDHOC is a lightweight authenticated key exchange protocol for IoT communication, currently being standardized by the IETF. Its design is a trimmed-down version of similar protocols like TLS 1.3, building on the SIGn-then-MAc (SIGMA) rationale. In its trimming, however, EDHOC notably deviates from the SIGMA design by sending only short, non-unique credential identifiers, and letting recipients perform trial verification to determine the correct communication partner. Done naively, this can...

Kyber is a key-encapsulation mechanism (KEM) that was recently selected by NIST in its PQC standardization process; it is also the only scheme to be selected in the context of public-key encryption (PKE) and key establishment. The main security target for KEMs, and their associated PKE schemes, in the NIST PQC context has been IND-CCA security. However, some important modern applications also require their underlying KEMs/PKE schemes to provide anonymity (Bellare et al., ASIACRYPT 2001)....

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...

Biometric data are uniquely suited for connecting individuals to their digital identities. Deriving cryptographic key exchange from successful biometric authentication therefore gives an additional layer of trust compared to password-authenticated key exchange. However, biometric data are sensitive personal data that need to be protected on a long-term basis. Furthermore, efficient feature extraction and comparison components resulting in high intra-subject tolerance and inter-subject...

Authenticated key-exchange (AKE) protocols are an important class of protocols that allow two parties to establish a common session key over an insecure channel such as the Internet to then protect their communication. They are widely deployed in security protocols such as TLS, IPsec and SSH. Besides the confidentiality of the communicated data, an orthogonal but increasingly important goal is the protection of the confidentiality of the identities of the involved parties (aka privacy). For...

Privacy-Preserving Authenticated Key Exchange (PPAKE) provides protection both for the session keys and the identity information of the involved parties. In this paper, we introduce the concept of robustness into PPAKE. Robustness enables each user to confirm whether itself is the target recipient of the first round message in the protocol. With the help of robustness, a PPAKE protocol can successfully avoid the heavy redundant communications and computations caused by the ambiguity of...

Over the last years, the side-channel analysis of Post-Quantum Cryptography (PQC) candidates in the NIST standardization initiative has received increased attention. In particular, it has been shown that some post-quantum Key Encapsulation Mechanisms (KEMs) are vulnerable to Chosen-Ciphertext Side-Channel Attacks (CC-SCA). These powerful attacks target the re-encryption step in the Fujisaki-Okamoto (FO) transform, which is commonly used to achieve CCA security in such schemes. To...

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...

Authenticated Key Exchange (AKE) is a cryptographic protocol to share a common session key among multiple parties. Usually, PKI-based AKE schemes are designed to guarantee secrecy of the session key and mutual authentication. However, in practice, there are many cases where mutual authentication is undesirable such as in anonymous networks like Tor and Riffle, or difficult to achieve due to the certificate management at the user level such as the Internet. Goldberg et al. formulated a model...

Implantable Medical Devices (IMDs) are widely deployed today and often use wireless communication. Establishing a secure communication channel to these devices is vital, however, also challenging in practice. To address this issue, numerous researchers have proposed IMD key exchange protocols, in particular ones that leverage an Out-Of-Band (OOB) channel such as audio, vibration and physiological signals. These solutions have advantages over traditional key exchange, e.g.,...

We study witness-authenticated key exchange (WAKE), in which parties authenticate through knowledge of a witness to any NP statement. WAKE achieves generic authenticated key exchange in the absence of trusted parties; WAKE is most suitable when a certificate authority is either unavailable or undesirable, as in highly decentralized networks. In practice WAKE approximates witness encryption, its elusive non-interactive analogue, at the cost of minimal interaction. This work is the first to...

We model and analyze the Signal end-to-end secure messaging protocol within the Universal Composability (UC) framework. Specifically: (1) We formulate an ideal functionality that captures end-to-end secure messaging in a setting with Public Key Infrastructure (PKI) and an untrusted server, against an adversary that has full control over the network and can adaptively and momentarily compromise parties at any time, obtaining their entire internal states. Our analysis captures the forward...

Key exchange protocols from the learning with errors (LWE) problem share many similarities with the Diffie–Hellman–Merkle (DHM) protocol, which plays a central role in securing our Internet. Therefore, there has been a long time effort in designing authenticated key exchange directly from LWE to mirror the advantages of DHM-based protocols. In this paper, we revisit signal leakage attacks and show that the severity of these attacks against LWE-based (authenticated) key exchange is still...

In this paper we investigate the field of privacy-preserving authenticated key exchange protocols (PPAKE). First we make a cryptographic analysis of a previous PPAKE protocol. We show that most of its security properties, including privacy, are broken, despite the security proofs that are provided. Then we describe a strong security model which captures the security properties of a PPAKE: entity authentication, key indistinguishability, forward secrecy, and privacy. Finally, we present a...

The Transport Layer Security (TLS) protocol is a fundamental building block for ensuring security on Internet. It provides an easy to use framework for the purposes of establishing an authenticated and secure channel between two parties that have never physically met. Nevertheless, TLS only provides a simple cryptographic functionality compared to more advanced protocols such as protocols for secure multiparty computation (MPC). In this work, we provide a framework for efficiently...

We give a cryptographic analysis of the Bluetooth Secure Connections Protocol Suite. Bluetooth supports several subprotocols, such as Numeric Comparison, Passkey Entry, and Just Works, in order to match the devices' different input/output capabilities. Previous analyses (e.g., Lindell, CT-RSA'09, or Troncoso and Hale, NDSS'21) often considered (and confirmed) the security of single subprotocols only. Recent practically verified attacks, however, such as the Method Confusion Attack (von...

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...

Recently, motivated by its increased use in real-world applications, there has been a growing interest on the reduction of trust in the generation of the common reference string (CRS) for zero-knowledge (ZK) proofs. This line of research was initiated by the introduction of subversion non-interactive ZK (NIZK) proofs by Bellare et al. (ASIACRYPT'16). Here, the zero-knowledge property needs to hold even in case of a malicious generation of the CRS. Groth et al. (CRYPTO'18) then introduced the...

Robust (fuzzy) extractors are very useful for, e.g., authenticated exchange from shared weak secret and remote biometric authentication against active adversaries. They enable two parties to extract the same uniform randomness with the ``helper'' string. More importantly, they have an authentication mechanism built in that tampering of the ``helper'' string will be detected. Unfortunately, as shown by Dodis and Wichs, in the information-theoretic setting, a robust extractor for an...