The onion routing (OR) network Tor provides anonymity to its users by routing their encrypted traf-fic through three proxies (or nodes). The key cryptographic challenge, here, is to establish symmetric session keys using a secure key exchange between the anonymous users and the selected nodes. The Tor network currently employs a one-way authenticated key exchange (1W-AKE) protocol ntor for this purpose. Nevertheless, ntor as well as other known 1W-AKE protocols rely solely on some classical Diffie-Hellman (DH) type assumptions for their (forward) security, and thus privacy of today’s anony-mous communication cannot be ensured once quantum computers arrive. In this paper, we demonstrate utility of quantum-secure lattice-based cryptography towards solving this problem for onion routing. In particular, we present a novel hybrid 1W-AKE protocol (HybridOR) that is secure under the lattice-based ring learning with error (ring-LWE) assumption as well as the gap DH assumption. Due to its hybrid design, HybridOR is not only resilient against quantum attacks but also allows the OR nodes to use the current DH public keys and subsequently requires no modification to the current Tor public key infrastructure. Moreover, thanks to the recent progress in lattice-based cryp-tography in the form of efficient ring-based constructions, our protocol is also computationally more efficient than the currently employed 1W-AKE protocol ntor, and it only introduces small and manage-able communication overhead to the Tor protocol.
The onion routing (OR) network Tor provides anonymity to its users by routing their encrypted traf-fic through three proxies (or nodes). The key cryptographic challenge, here, is to establish symmetric session keys using a secure key exchange between the anonymous users and the selected nodes. The Tor network currently employs a one-way authenticated key exchange (1W-AKE) protocol ntor for this purpose. Nevertheless, ntor as well as other known 1W-AKE protocols rely solely on some classical Diffie-Hellman (DH) type assumptions for their (forward) security, and thus privacy of today’s anony-mous communication cannot be ensured once quantum computers arrive. In this paper, we demonstrate utility of quantum-secure lattice-based cryptography towards solving this problem for onion routing. In particular, we present a novel hybrid 1W-AKE protocol (HybridOR) that is secure under the lattice-based ring learning with error (ring-LWE) assumption as well as the gap DH assumption. Due to its hybrid design, HybridOR is not only resilient against quantum attacks but also allows the OR nodes to use the current DH public keys and subsequently requires no modification to the current Tor public key infrastructure. Moreover, thanks to the recent progress in lattice-based cryp-tography in the form of efficient ring-based constructions, our protocol is also computationally more efficient than the currently employed 1W-AKE protocol ntor, and it only introduces small and manage-able communication overhead to the Tor protocol.
Anonymous communication networks (ACNs) enable Internet browsing in a way that prevents accessed content from being traced back to the user. This provides a high level of privacy, protecting individuals from being tracked by advertisers, governments, and other entities. The Tor network, a prominent example of such a network, uses a layered encryption scheme to encapsulate data packets, employing Tor nodes to obscure the routing process before the packets enter the public Internet. While Tor is capable of providing substantial privacy, its encryption relies on schemes such as RSA and Diffie-Hellman for distributing symmetric keys, which are vulnerable to quantum computing attacks and are currently in the process of being phased out. To overcome this threat, we propose a quantum resistant alternative to RSA and Diffie-Hellman for distributing symmetric keys, namely, quantum key distribution (QKD). Standard QKD networks depend on trusted nodes to relay keys across long distances. However, reliance on trusted nodes in the quantum network does not meet the criteria necessary for establishing a Tor circuit in the ACN. We address this issue by developing a protocol and network architecture that integrates QKD without the need for trusted nodes, thus meeting the requirements of the Tor network and creating a quantum secure anonymous communication network.
The necessity of a secure key exchange protocol arises from the critical need to establish encrypted communication over an untrusted network. Over time, a multitude of key exchange mechanisms have been developed to counteract adversarial threats. The Diffie-Hellman key exchange protocol (DHKE) is one of the most widely used protocols for symmetric key sharing. However, this protocol exhibits certain inherent limitations that attackers may exploit. It lacks authentication mechanism and is susceptible to Man-in-the-Middle (MITM) attacks and quantum attacks. To mitigate these vulnerabilities, we have designed a hybrid key exchange protocol combining DHKE with Learning With Errors (LWE), a lattice-based post-quantum primitive. This proposed protocol provides authentication via a Public Key Infrastructure (PKI) together with CRYSTALS-Dilithium digital signature, resilience against MITM attacks, and robustness against classical and quantum threats. We have done a security analysis using the Dolev-Yao threat model, extended to quantum-equipped attackers, and showed that the protocol achieves mutual authentication, session key secrecy, and forward secrecy under the hardness of LWE and DHKE. Lastly, we provided detailed parameter recommendations based on NIST standards and shed light on side-channel attacks.
Objective: To design a secure and efficient three-party post-quantum authenticated key agreement (AKE) protocol that ensures mutual authentication, user anonymity, and forward secrecy, while resisting both classical and quantum adversaries. Methods: The proposed protocol is constructed using the Ring Learning with Errors (Ring-LWE) assumption, which is widely regarded as quantum-resistant. The scheme enables two users to establish a shared session key through a trusted server over an insecure channel. Cryptographic hash functions, lattice-based operations, and masking techniques are employed to achieve authentication, anonymity, and key confidentiality. Formal correctness proofs, informal security analysis, and comparative performance evaluations are conducted to validate the protocol. Findings: The study describes qualitative benefits like "outperforms current protocols" but lacks specific metrics, such as exact computation costs (e.g., 4913 ns total execution) or communication rounds, and "reduces user-side cost to 2438 ns vs. 5395 ns in Islam et al.". Also, substantially more efficient than pairing- or chaotic-map-based protocols, which incur costs exceeding 12000 ns. Communication overhead is reduced by limiting the exchange to two RLWE-based messages and one server response, avoiding expensive bilinear pairing or biometric hash transmissions. These results demonstrate that the proposed scheme provides stronger security guarantees at a lower computational and communication cost, making it suitable for resource-constrained mobile and IoT environments. Novelty: Unlike existing approaches, the proposed protocol simultaneously guarantees user anonymity, forward secrecy, and quantum resistance in a three-party setting based on Ring-LWE. It overcomes known vulnerabilities in prior schemes and achieves improved efficiency without compromising security, making it a practical and robust solution for post-quantum secure communications. Keywords: Key Establishment, Authentication, Ring Learning with Errors, Anonymous Key Exchange, Post Quantum Forward Secrecy
Authenticated key exchange (AKE) is a crucial cryptographic primitive used for establishing an authenticated and confidential communication channel between parties, which has been widely used in our daily life when we surf on the Internet. However, in past decades mutual AKE protocols have been studied extensively in theory, while in many practical environments such as in the Tor anonymity network the mutual authentication property is undesirable. Meanwhile, considering privacy protection is getting more and more attention and one-way AKE protocols play an important role in privacy protection, so no matter in theory or in practice, it is quite meaningful to conduct research on the one-way AKE protocols. In this article, we present a new efficient anonymous one-way AKE protocol, which has strong anonymity and security properties guarantee, and efficiency advantages. Moreover, our new scheme has tight security reduction and is formally proved secure in the random oracle model under the Gap-DH and XCR signature security assumptions.
The advancement of quantum computing threatens classical cryptographic methods, necessitating the development of secure quantum key distribution (QKD) solutions for QKD Networks (QKDN). In this paper, a novel key distribution protocol, Onion Routing Relay (ORR), that integrates onion routing (OR) with post-quantum cryptography (PQC) in a key-relay (KR) model is evaluated for QKDNs. This approach increases the security by enhancing confidentiality, integrity, authenticity (CIA principles), and anonymity in quantum-secure communications. By employing PQC-based encapsulation, ORR aims to avoid the security risks posed by intermediate malicious nodes and ensures end-to-end security. Our results show a competitive performance of the basic ORR model, against current KR and trusted-node (TN) approaches, demonstrating its feasibility and applicability in high-security environments maintaining a consistent Quality of Service (QoS). The results also show that while basic ORR incurs higher encryption overhead, it provides substantial security improvements without significantly impacting the overall key distribution time. Nevertheless, the introduction of an end-to-end authentication extension (ORR-Ext) has a significant impact on the Quality of Service (QoS), thereby limiting its suitability to applications with stringent security requirements.
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 of anonymous one-sided AKE which guarantees the anonymity of the client by allowing only the client to authenticate the server, and proposed a concrete scheme. However, existing anonymous one-sided AKE schemes are only known to be secure in the random oracle model. In this paper, we propose generic constructions of anonymous one-sided AKE in the random oracle model and in the standard model, respectively. Our constructions allow us to construct the first post-quantum anonymous one-sided AKE scheme from isogenies in the standard model.