Secure Remote Password (SRP) protocol is an essential password-authenticated key exchange (PAKE) protocol based on the discrete logarithm problem (DLP). The protocol is specifically designed to obtain a session key and it has been widely used in various scenarios due to its attractive security features. In the SRP protocol, the server is not required to save any data directly associated with passwords. And this makes attackers who manage to corrupt the server fail to impersonate the client unless performing a brute-force search for the password. However, the development of quantum computing has potentially made classic DLP-based public-key cryptography schemes not secure, including the SRP protocol. So it is significant to design a quantum-resistant SRP protocol. In this paper, based on the original scheme, we propose a post-quantum SRP protocol from the learning with errors (LWE) problem. And we give rigorous proof and analyses on the correctness and security of the scheme. Besides being resistant to known quantum attacks, it maintains the various secure qualities of the original protocol.
Secure Remote Password (SRP) protocol is an essential password-authenticated key exchange (PAKE) protocol based on the discrete logarithm problem (DLP). The protocol is specifically designed to obtain a session key and it has been widely used in various scenarios due to its attractive security features. In the SRP protocol, the server is not required to save any data directly associated with passwords. And this makes attackers who manage to corrupt the server fail to impersonate the client unless performing a brute-force search for the password. However, the development of quantum computing has potentially made classic DLP-based public-key cryptography schemes not secure, including the SRP protocol. So it is significant to design a quantum-resistant SRP protocol. In this paper, based on the original scheme, we propose a post-quantum SRP protocol from the learning with errors (LWE) problem. And we give rigorous proof and analyses on the correctness and security of the scheme. Besides being resistant to known quantum attacks, it maintains the various secure qualities of the original protocol.
Abstract In order to solve the issue that traditional secure remote password (SRP) protocols cannot resist the active quantum computing attack, a simple and efficient SRP protocol based on post quantum algorithm Kyber named KSRP is proposed. In the protocol, the asymmetrical key consensus algorithm (AKCN) and post quantum algorithm are used to implement authenticated key exchange. This scheme can resist password recovery, Denning-Sacco’s attack and other attacks after being analyzed, which satisfies provable security under eCK model and indistinguishable game model. Compared with the traditional password authenticated key exchange (PAKE) protocols based on classical hard mathematical problems, this protocol refers to the generation method on the temporary public key and private key in the post quantum public key encryption algorithm Kyber, which enhances the security of process parameters. In addition, the scheme uses compression functions for the transmitted session public key to reduce communication overhead and improve security. After being tested in the LWE tester tool SageMathCell, the security of this protocol can reach 313 bits, which is 2.79 times the traditional SRP protocol, and 3.91 times J-PAKE protocol, also is higher 70.1% than Ding’s RLWE-PAK and RLWE-PPK protocols. The communication overhead in the protocol is only higher about 16% of post-quantum PPK and PAK protocols. This protocol is simple, efficient, and resistant to quantum computing active attacks, which can be applied in remote authenticated key exchange in cloud networks.
Abstract Password‐authenticated key exchange ( PAKE ) is a cryptographic primitive that can establish secure remote communications between the client and the server, especially with the advantage of amplifying memorable passwords into strong session keys. However, the arrival of the quantum computing era has brought new challenges to traditional PAKE protocols. Thus, designing an efficient post‐quantum PAKE scheme becomes an open research question. In this paper, the authors construct a quantum‐safe PAKE protocol, which is a horizontal extension of the password‐authenticated key (PAK) protocol in the field of module lattices. Subsequently, the authors accompany the proposed protocol with a rigorous security proof in the random oracle model with two adaptions: applying the CDF‐Zipf model to characterise the ability of the adversary and using the pairing with errors assumption to simplify the proof. Taking the flexibility of the module learning with errors ( MLWE ) problem, the authors elaborately select three parameter sets to meet different application scenarios. Specifically, the authors’ Recommended‐PAKE implementation achieves 177‐bit post‐quantum security with a generous margin to cope with later improvement in cryptanalysis. The performance results indicate that the authors’ MLWE‐PAKE is quite practical: compared with the latest Yang‐PAK , the authors’ Recommended‐PAK reduces the communication cost and the running time by 36.8% and 13.8%, respectively.
Password authentication is a prevalent method of user verification across the Internet, and its use extends to scenarios where resources are limited. However, current password authentication protocols primarily rely on traditional password authenticated key exchange (PAKE) protocols (e.g., SRP, OPAQUE), which are vulnerable to attacks by quantum adversaries. To date, no efficient quantum algorithm has been found to solve the common challenges in lattice-based cryptography. Therefore, quantum-resistant PAKE protocols are generally built upon lattice-based cryptography. In this work, we propose a threshold verifiable oblivious pseudorandom function () protocol based on secret sharing. We then integrate it into a PAKE protocol and present an instantiation of a quantum-safe threshold PAKE protocol () based on the Ring Learning with Errors (RLWE) assumption. This integration gives our PAKE protocol resistance to precomputation attacks, similar to OPAQUE. Furthermore, by incorporating thresholding techniques into the PAKE protocol, we mitigate the risk of single points of failure on the server side. Our protocol not only preserves the security guarantees of traditional PAKE schemes but also resists attacks from quantum adversaries. We also provide a comprehensive security analysis and evaluation of, providing valuable insights for its practical implementation.
The advent of quantum computing presents significant challenges to current cryptographic systems, particularly those based on the Discrete Logarithm Problem (DLP), which underpins the security of many cryptocurrencies. In response, we propose a quantum-resistant adaptation of the Updatable Public Key (UPK) primitive in the Quisquis cryptocurrency protocol. This adaptation transitions from a DLP-based security model to one grounded in the Learning With Errors (LWE) assumption, which is believed to be secure against quantum attacks. Our LWE-based UPK scheme preserves the key advantages of Quisquis, including the ability to update public keys in a publicly verifiable manner while maintaining their indistinguishability from freshly generated keys. We discuss the challenges introduced by this transition, particularly the accumulation of noise during key updates, and outline future work to address these issues. Our work ensures that Quisquis remains a robust and efficient solution for privacy-preserving transactions in a post-quantum world.
The rapid development of quantum computers poses a significant threat to the majority of current authenticated key exchang protocols, designed on the hardness of large integer factorization and discrete logarithm problems. Therefore, it is imperative to develop secure and efficient quantum-resistant authenticated key exchang protocols. This paper designs a new public-key cryptographic scheme for identity authentication based on Ring Learning With Errors (RLWE) problem and error reconciliation mechanism. Based on the scheme, we further design a quantum-resistant authenticated key exchange protocol (AKE). This protocol is provably secure under the standard eCK model and achieves forward secrecy. Compared with other classic key exchange protocols based on the RLWE problem, our protocol shows comprehensive advantages in terms of security, computational complexity, and communication complexity.
A three-party authenticated key exchange protocol enables two entities to agree on a session key with the help of a dedicated server over public channel. Shor’s algorithm is a big threat for existing authenticated key exchange protocols. Lattice based cryptography plays a very important role in designing authentication and key agreement secure against the threat of quantum attacks. However, it is not easy job to design quantum resistant password based three party protocol due to the high demand for security requirements and the limited resources nature of mobile devices. In this article, we have proposed a new post quantum three party key exchange based on ring learning with errors assumption. This protocol is motivated from Islam et al.’s authenticated key exchange protocol. Their protocol is not secure against stolen smartcard attack, password guessing attack, and can’t provide user anonymity. The anonymous communication is a big requirement for practical applications like e-healthcare services/smart vehicular communication. This paper also contains the performance analysis of the proposed protocol along with other relevant protocols.