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 to reason in the QROM, including the compressed oracle and the extractable QROM. To pave the way towards closing the gap, we then further identify an efficient simulator for the ideal cipher. This provides certain programming abilities as a necessary and sufficient condition to close the gap in the proof: we demonstrate that we can close the gap using the simulator, and give a meta-reduction based on KEM-anonymity that shows the impossibility of a non-programming reduction that covers a class of KEMs that includes Kyber / ML-KEM.
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 to reason in the QROM, including the compressed oracle and the extractable QROM. To pave the way towards closing the gap, we then further identify an efficient simulator for the ideal cipher. This provides certain programming abilities as a necessary and sufficient condition to close the gap in the proof: we demonstrate that we can close the gap using the simulator, and give a meta-reduction based on KEM-anonymity that shows the impossibility of a non-programming reduction that covers a class of KEMs that includes Kyber / ML-KEM.
Encrypted key exchange (EKE), introduced by Bellovin and Merritt (IEEE S\&P 1992), and Masny-Rindal OT, introduced by Masny and Rindal (ACM CCS 2019), are highly-efficient methods for compiling essentially any KEM into advanced cryptographic protocols, namely password-authenticated key exchange (PAKE) and oblivious transfer (OT), by relying only on idealized symmetric-key primitives. They have become leading candidates for practically-implementable PAKE and OT due to (1) their simplicity, (2) their plug-and-play nature, allowing for flexibility in the choice of KEM, and (3) existing proofs of UC-security (in the classical adversarial model).
Due to point (2) above, these compilers yield attractive candidates for efficient \emph{post-quantum} PAKE and OT, especially given the recent post-quantum KEM standardization efforts. This motivates the question of whether the (UC-)security of these compilers translates to the quantum adversarial model. In this work, we show that it does not. In particular, we prove that a general family of (O)EKE protocols, as well as Masny-Rindal OT, are \emph{not} UC-secure against quantum polynomial-time adversaries, even when instantiated with a post-quantum KEM. To establish UC-insecurity, we devise an adversarial strategy that provably thwarts any attempt by the simulator to extract its input (the password in the case of PAKE, and the receiver's choice bit in the case of OT).
To complement these negative results, we establish that both compilers yield certain notions of \emph{game-based} security. Along the way, we establish a novel ``advantage-tight'' one-way to hiding lemma that may be of independent interest.
Driven by advances in the standardization of NIST’s Post-Quantum Cryptography (PQC) algorithms, research on constructing Password Authenticated Key Exchange (PAKE) protocols using Key Encapsulation Mechanisms (KEMs) has gained considerable attention. Several PAKE protocols have established precise security requirements for the underlying KEM. Arriaga et al. introduced a PAKE protocol called CHIC, which requires the KEM to achieve anonymity under plaintext-checkable attacks (ANO-1PCA). An anonymous KEM does not leak any information about which public key was used for encryption. It protects the identities and privacy of participants and is critical in preventing identity-guessing attacks, therefore, anonymity is also called key-privacy. The anonymity of NIST PQC Round-3 candidates has recently been analyzed, some of which satisfied ANO-CCA.Huguenin-Dumittan and Vaudenay proposed two efficient constructions, TCHand TH, to create KEM from public-key encryption (PKE) schemes. Jiang et al. introduced TRHbased on TH. These constructions can transform any OW-CPA PKE into an IND-qCCA KEM efficiently and avoid re-encryption. However, prior to this work, no research has been conducted to determine whether these constructions preserve or lift anonymity.In this paper, we proved that for any OW-CPA, DS-IND PKE, the construction KEMRH= TRH[PKE,H] achieves ANO1-CCA in the quantum random oracle model (QROM). We then construct a KEM called KyberRH, and provide an algorithm for the CHIC protocol using KyberRH.
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 Non-uniform LWE and the Weak-Hint LWE assumptions, as well as its application to Ring and Module LWE. Finally, we show how to obtain a secure PAKE from our construction with concrete parameter choices for lattice KEMs.
Recent developments in quantum computers pose an imminent threat to cryptography since many widely used cryptographic schemes will no longer be secure. This worrisome scenario motivated a growing interest in the field of post-quantum cryptography, which aims to design cryptosystems that are postquantum secure, i.e. secure against quantum-capable adversaries. While finding post-quantum computational hardness assumptions is pivotal to achieve this goal, an issue that is often overlooked is provable security. In fact, to prove that the post-quantum computational hardness necessarily implies post-quantum security of the derived cryptosystem, the reduction argument that establishes this implication also needs to be post-quantum. As such, many new methods have been devised in the last few years to handle this adaptation to the quantum setting. In particular, the quantum analogue of the Random Oracle Model has garnered special interest, as it is the foundation of many cryptographic schemes, from public-key encryption to digital signatures. It is also very problematic and usually the main culprit of the failure of security proofs when transitioning to the quantum setting. This work offers a comprehensive exposition on the most influential techniques developed in the last decade to enable or facilitate the construction of security proofs in the Quantum Random Oracle Model (QROM). Each presented technique offers an unique purpose and a solution to a problem provoked by the QROM, and, as such, as a whole, this works allows for an understanding of the most common strategies to construct these type of security proofs. This is accomplished by presenting and analyzing the security proof of three cryptographic schemes set in this model, which underlines the central role these techniques take in provable quantum security.
Transport Layer Security (TLS) protocols are essential for ensuring the confidentiality, integrity, and authentication of data communications. Mutual authentication between client and server is crucial in high-security scenarios such as finance and government. However, existing TLS protocols typically rely on certificate-based public key infrastructures (PKI) for client authentication, which increases deployment complexity and introduces risks associated with third-party trust. In contrast, password-authenticated TLS protocols use memorable passwords for client authentication, offering advantages in simplicity and usability. Nonetheless, such protocols remain vulnerable to server compromise and fail to provide sufficient security against quantum adversaries.To address these challenges, we propose a novel TLS protocol based on asymmetric password-authenticated key exchange (PAKE). The protocol employs an asymmetric PAKE mechanism wherein only password-derived information is stored on the server, while the client derives its private key from the password. This design effectively mitigates the risk of server leakage attacks. The protocol further integrates two types of post-quantum secure key encapsulation mechanisms (KEMs): an OW-ChCCA (One-Way Checkable against Chosen-Ciphertext Attacks) secure KEM for server key exchange and authentication, and an OW-PCA (One-Way Plaintext-Checkable Attacks) secure KEM for binding the client’s password-derived private key to enable client authentication. Both KEMs support multi-user, multi-challenge settings and admit tight, post-quantum secure instantiations.Furthermore, this paper provides a formal security analysis of the proposed protocol within an optimized multi-stage key exchange model. By combining the random oracle and ideal cipher models with a game-based proof methodology, we demonstrate that the protocol achieves mutual authentication and forward secrecy, while also providing tight security bounds and post-quantum resilience. This work thus presents a promising solution for constructing post-quantum password-authenticated TLS protocols.
Password Authenticated Key Exchange (PAKE) establishes secure communication channels using passwords for authentication. Currently, standardized PAKEs rely on classical asymmetric cryptography. However, these 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 Cryptography (PQC) integration efforts. Hence, there is a significant awareness gap compared to PQC primitives subject to the official standardization processes. We provide a comprehensive overview of existing PQC PAKEs, classify their design rationales and authentication methods, and address aspects related to their security and performance. We identify PAKE designs that are still unexplored in the PQC realm and discuss the possibility of their adaptation. Thus, we offer a detailed reference for future work on PQC PAKEs.