Summary Key exchange protocols play an important role in securing the network communication over an insecure channel. In literature, a large number of key exchange schemes exist. The security of most of them is based on the Diffie‐Hellman (DH) problems over a group. But these types of DH problems are solvable in the presence of quantum computers. Thus, we require a non‐DH type key exchange scheme that resists to the quantum computers and new modern technologies. In this paper, 2 novel lattice‐based authenticated key exchange (LB‐AKE) protocols, (1) using a signature‐based authenticator and (2) using a signcryption‐based authenticator, are devised in Canetti‐Krawczyk proof model. The security of proposed protocols depends on the hardness of small integer solutions on the lattice. An extensive proof of security to our claim is given. The proposed AKEs characterize faster computation speed and resistance to the modern complex computers.
Summary Key exchange protocols play an important role in securing the network communication over an insecure channel. In literature, a large number of key exchange schemes exist. The security of most of them is based on the Diffie‐Hellman (DH) problems over a group. But these types of DH problems are solvable in the presence of quantum computers. Thus, we require a non‐DH type key exchange scheme that resists to the quantum computers and new modern technologies. In this paper, 2 novel lattice‐based authenticated key exchange (LB‐AKE) protocols, (1) using a signature‐based authenticator and (2) using a signcryption‐based authenticator, are devised in Canetti‐Krawczyk proof model. The security of proposed protocols depends on the hardness of small integer solutions on the lattice. An extensive proof of security to our claim is given. The proposed AKEs characterize faster computation speed and resistance to the modern complex computers.
A key exchange protocol is an important primitive in the field of information and network security and is used to exchange a common secret key among various parties. A number of key exchange protocols exist in the literature and most of them are based on the Diffie-Hellman (DH) problem. But, these DH type protocols cannot resist to the modern computing technologies like quantum computing, grid computing etc. Therefore, a more powerful non-DH type key exchange protocol is required which could resist the quantum and exponential attacks. In the year 2013, Lei and Liao, thus proposed a lattice-based key exchange protocol. Their protocol was related to the NTRU-ENCRYPT and NTRU-SIGN and so, was referred as NTRU-KE. In this paper, we identify that NTRU-KE lacks the authentication mechanism and suffers from the man-in-the-middle (MITM) attack. This attack may lead to the forging the authenticated users and exchanging the wrong key.
The most widely accepted models in the security proofs of authenticated key exchange protocols are the Canetti–Krawczyk (CK) and extended CK models that admit different adversarial queries with ambiguities and incomparable strength. It is desirable to incorporate specific and powerful adversarial queries into a single unified security model and establish a more practical oriented security notion. Concerning the security of one‐round implicitly authenticated Diffie–Hellman (DH) key exchange protocols, the authors present a unified security model that has many advantages over the previous ones. In the model, a system environment is set up, all of adversarial queries are practically interpreted and definitely characterised through physical environment, and some rigorous rules of secret leakage are also specified. To demonstrate usability of their model, a new protocol based on the OAKE protocol is proposed, which satisfies the presented strong security notion and attains high efficiency. The protocol is proven secure in random oracle model under gap DH assumption.
Using the hard assumption of Ring-Decision Learning With Errors (DLWE) in the lattice, we propose a new authenticated key exchange (AKE) scheme which is based on Peikert’s reconciliation technique. Under the CK+ model, the proposed scheme is provably secure. Compared with the traditional Diffie-Hellman (DH) authenticated key exchange (AKE) schemes, the proposed scheme not only has better efficiency and stronger security but also resists quantum attacks because of the hard assumption on lattice problem. The comparisons between Ring-LWE based ones shows that the proposed scheme protects the shared session key with balanced key derivation function (KDF) compared with those current AKE schemes from LWE.
Abstract. Public key exchange protocol is identified as an important application in the field of public-key cryptography. Most of the existing public key exchange schemes are Diffie-Hellman (DH)-type, whose security is based on DH problems over different group-s. Note that there exists Shor’s polynomial-time algorithm to solve these DH problems when a quantum computer is available, we are therefore motivated to seek for a non-DH-type and quantum resistant key exchange protocol. To this end, we turn our attention to lattice-based cryptography. The higher methodology behind our roadmap is that in anal-ogy to the link between ElGamal, DSA, and DH, one should expect a NTRU lattice-based key exchange primitive in related to NTRU-ENCRYPT and NTRU-SIGN. However, this excepted key exchange protocol is not presented yet and still missing. In this paper, this missing key exchange protocol is found, hereafter referred to as NTRU-KE, which is stud-ied in aspects of security and key-mismatch failure. In comparison with ECDH (Elliptic Curve-based Diffie-Hellman), NTRU-KE features faster computation speed, resistance to quantum attack, and more communication overhead. Accordingly, we come to the conclu-sion that NTRU-KE is currently comparable with ECDH. However, decisive advantage of NTRU-KE will occur when quantum computers become a reality.
Abstract. An unresolved problem in research on authenticated key exchange (AKE) is to construct a secure protocol against advanced attacks such as key compromise impersonation and maximal exposure attacks without relying on random oracles. HMQV, a state of the art AKE protocol, achieves both efficiency and the strong security proposed by Krawczyk (we call it the CK + model), which includes resistance to advanced attacks. However, the security proof is given under the random oracle model. We propose a generic construction of AKE from a key encapsulation mechanism (KEM). The construction is based on a chosen-ciphertext secure KEM, and the resultant AKE protocol is CK + secure in the standard model. The construction gives the first CK + secure AKE protocols based on the hardness of integer factorization problem, code-based problems, or learning problems with errors. In addition, instantiations under the Diffie-Hellman assumption or its variant can be proved to have strong security without non-standard assumptions such as πPRF and KEA1. Furthermore, we extend the CK + model to identity-based (called the id-CK + model), and propose a generic construction of identity-based AKE (ID-AKE) based on identity-based KEM, which satisfies id-CK + security. The construction leads first strongly secure ID-AKE protocols under the hardness of integer factorization problem, or learning problems with errors.
Abstract Authenticated multiple key agreement (AMKA) protocols provide participants with multiple session keys after one round of authentication. Many schemes use Diffie–Hellman or authenticated key agreement schemes that rely on hard integer factorizations that are vulnerable to quantum algorithms. Lattice cryptography provides quantum resistance to authenticated key agreement protocols, but the certificate always incurs excessive public key infrastructure management overhead. Thus, a lightweight lattice‐based secure system is needed that removes this overhead. To answer this need, we provide a two‐party lattice‐ and identity‐based AMKA scheme based on bilateral short integer or computational bilateral inhomogeneous small integer solutions, and we provide a security proof based on the random oracle model. Compared with existing AMKA protocols, our new protocol has higher efficiency and stronger security.