On the Multi-user Security of LWE-Based NIKE

Shuai Han, Shengli Liu, Zhedong Wang +1 more

Yun Wei, Fushan Wei, Chuangui Ma

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.

Huiwen Jia, Yupu Hu

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.

Jonathan Bootle, Mehdi Tibouchi, Keita Xagawa

Alex Lombardi, Ethan Mook, Willy Quach +1 more

Yupu Hu, Huiwen Jia

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.