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International Conference on Availability, Reliability and Security (ARES)

Non-Interactive Key Exchange from Identity-Based Encryption

Olivier Blazy, Céline Chevalier

Published Aug 13, 2018• 5 citations
Publisher

Abstract

Since the seminal work of Diffie and Hellman [19], Non-Interactive Key Exchange (NIKE) has become one of the fundamental problems of modern cryptography, but additional security requirements have led to elaborated ad-hoc constructions, which often lack simplicity in their design. In particular, Identity-Based NIKE is still a major problem with few available constructions, and those ad-hoc constructions do not give a lot of insight on what is required to be able to achieve such a NIKE scheme only based on the identity (and not relying on the public-key setting).

DOI
10.1145/3230833.3230864

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Since the seminal work of Diffie and Hellman [19], Non-Interactive Key Exchange (NIKE) has become one of the fundamental problems of modern cryptography, but additional security requirements have led to elaborated ad-hoc constructions, which often lack simplicity in their design. In particular, Identity-Based NIKE is still a major problem with few available constructions, and those ad-hoc constructions do not give a lot of insight on what is required to be able to achieve such a NIKE scheme only based on the identity (and not relying on the public-key setting).
Non-interactive key exchange (NIKE) allows two parties to establish a shared key without communications. In ID-based non-interactive key exchange (ID-NIKE) protocols, private key generator (PKG) knows user's private key, so it can calculate the shared key between two participants, and most constructions of ID-NIKE need expensive pairing operation. To overcome these disadvantages, a security model of certificateless non-interactive key exchange (CL-NIKE) is proposed in this paper. And a scheme without pairings is also given. The proposed protocol is proved secure in the Random Oracle Model (ROM) based on the gap Diffie-Hellman (GDH) and computational Diffie-Hellman (CDH) problem. In the new protocol, key generation center (KGC) only knows user's partial key and is not able to calculate the shared key. Moreover, the new protocol is more efficient than the existing ID-NIKE schemes because it is pairing-free.
Non-interactive key exchange (NIKE) enables two or multiple parties (just knowing the public system parameters and each other's public key) to derive a (group) session key without the need for interaction. Recently, NIKE in multi-party settings has been attached importance. However, we note that most existing multi-party NIKE protocols, underlying costly cryptographic techniques (i.e., multilinear maps and indistinguishability obfuscation), lead to high computational costs once employed in practice. Therefore, it is a challenging task to achieve multi-party NIKE protocols by using more practical cryptographic primitives. In this paper, we propose a secure and efficient NIKE protocol for secure communications in dynamic groups, whose construction only bases on bilinear maps. This protocol allows multiple parties to negotiate asymmetric group keys (a public group encryption key and each party's decryption key) without any interaction among one another. Additionally, the protocol supports updating of group keys in an efficient and non-interactive way once any party outside a group or any group member joins or leaves the group. Further, any party called a sender (even outside a group) intending to connect with some or all of group members called receivers in a group, just needs to generate a ciphertext with constant size under the public group encryption key, and only the group member who is the real receiver can decrypt the ciphertext to obtain the session key. We prove our protocol captures the correctness and indistinguishability of session key under k-Bilinear Diffie-Hellman exponent (k-BDHE) assumption. Efficiency evaluation shows the efficiency of our protocol.
The question of generalising the celebrated 2-party non-interactive key exchange (NIKE), Diffie-Hellman protocol, to a multipartite setting was left as an important open problem. In 2003, Boneh and Silverberg put forward a theoretical construction of multipartite NIKE protocol from a new notion called multilinear maps. In their protocol, however, the number of users N and the multilinearity k are related by N = k + 1, resulting in the system initialising another multilinear map when the number of users who want to exchange a session key changes. In this paper, we describe two extensional schemes of multipartite NIKE, which enables any less than or equal to N users derive a common shared key from an (N – 1)-multilinear map. In addition, using our extensional schemes, we show a concrete scenario: the establishment of any discussion group in a user group and its privacy version. Furthermore, we analyse its security.