Authenticated key exchange protocol under computational Diffie–Hellman assumption from trapdoor test technique

Abstract

This paper investigates authenticated key exchange (AKE) protocol under computational Diffie-Hellman assumption in the extended Canetti-Krawczyk model. The core technical component of our protocol is the trapdoor test technique, which is originally introduced to remove the gap Diffie-Hellman (GDH) assumption for the public key encryption schemes. Our contributions are twofold. First, we clarify some misunderstandings of the usage of the trapdoor test technique in AKE protocols showing its adaptation to the AKE protocols is not trivial. We point out some errors in some recent work which attempts to make use of the trapdoor test technique to remove GDH assumption. Second, based on trapdoor test technique, we propose an efficient extended Canetti-Krawczyk secure AKE protocol under computational Diffie-Hellman assumption instead of GDH assumption. Additionally, our protocol does not make use of NAXOS trick and has a tight reduction. In comparison with all existing AKE protocols with the properties as previously mentioned, our protocol with only three exponentiations is most efficient. the security on CDH assumption. Cash, Kiltz, and Shoup [3] proposed a new computational problem called twin Diffie-Hellman problem, at the heart of which is the 'trapdoor test', which is originally used to remove the gap assumption for the public key encryption schemes.Later, Huang et al. [4] first introduced this technique to remove the gap assumption for AKE protocol in eCK model. Some recent work [5,6] attempted to make use of the trapdoor test technique to construct eCK-secure AKE protocols under CDH assumption. However, there are several problems with the proofs, as will be discussed in section 3. Thus, we stress that the adaptation of the trapdoor test technique to the AKE protocols is not trivial and there are some pitfalls in the security proof. Actually, one of the purposes of this paper is to clarify the misusing of trapdoor test technique.Our Contributions This paper investigates eCK-secure AKE protocol under CDH assumption. Our contributions are twofold.First, the trapdoor test technique is a useful tool to remove the gap assumption in public key encryption schemes. Some people could think that it is trivial to adapt it to AKE protocols. However, we claim that this is not the case. We clarify some misunderstandings of the usage of the trapdoor test technique showing its adaptation to the AKE protocols is not trivial. We point out some errors in some recent work [5,6], which attempts to make use of the trapdoor test technique to remove gap assumption.Second, we proposes an efficient eCK-secure AKE protocol under CDH assumption. Additionally, our protocol does not make use of NAXOS trick ‡ and has a tight reduction. In comparison with all existing AKE protocols with the properties as previously mentioned, our protocol with only three exponentiations is most efficient.Our protocol requires the party to prove the knowledge of the static private key during the user registration phase, which was introduced earlier by Daisuke Moriy...

A novel and efficient lattice‐based authenticated key exchange protocol in C‐K model

“…To remove the difficulties of DH protocol, a number of authenticated key exchange (AKE) protocols [2][3][4][5][6][7] etc are proposed in the literature. In the year 1976, the idea of key exchange protocol is firstly given by Diffie and Hellman 1 in their seminal paper "New Directions in Cryptography."…”

“…Although the DH protocol itself is not an authentic key exchange protocol as it is insecure against a well-known man-in-the-middle (MITM) attack. To remove the difficulties of DH protocol, a number of authenticated key exchange (AKE) protocols [2][3][4][5][6][7] etc are proposed in the literature. These all proposed AKEs were implemented in traditional cryptography and either based on DH problem 1 or the elliptic curve DH problem.…”

PUF‐based solutions for secure communications in Advanced Metering Infrastructure (AMI)

“…Authenticated key exchange (AKE) and broadcast authentication (BA) protocols are cryptographic protocols that can assure the security of unicast and broadcast communications, respectively. In AKE protocols, 2 communicating parties are mutually authenticated; then a key is shared between them for encrypting the transmitted data to provide data confidentiality . Also, since the broadcasted commands by the utility to the smart meters through broadcast communication are critical, the smart meters must be assured that the received commands are broadcasted from an authorized entity and have not been altered.…”

“…In AKE protocols, 2 communicating parties are mutually authenticated; then a key is shared between them for encrypting the transmitted data to provide data confidentiality. [3][4][5][6][7] Also, since the broadcasted commands by the utility to the smart meters through broadcast communication are critical, the smart meters must be assured that the received commands are broadcasted from an authorized entity and have not been altered. Therefore, BA protocols are required to authenticate the broadcaster and the broadcasted messages.…”

Cryptanalysis and improvement of an efficient authenticated key exchange protocol with tight security reduction

“…In 2013, Yang [14] reasserted that the eCK model leaves out the definition of session state, which causes ambiguities that may yield a lot of potential problems. In resent years, many eCK-secure AKE protocols [15][16][17][18][19][20][21][22] are presented under eCK model, and many of them are insecure under the SessionStateReveal.…”