Full-Resilient Memory-Optimum Multi-Party Non-Interactive Key Exchange

Abstract

Multi-Party Non-Interactive Key Exchange (MP-NIKE) is a fundamental cryptographic primitive in which users register into a key generation centre and receive a public/private key pair each. After that, any subset of these users can compute a shared key without any interaction. Nowadays, IoT devices suffer from a high number and large size of messages exchanged in the Key Management Protocol (KMP). To overcome this, an MP-NIKE scheme can eliminate the airtime and latency of messages transferred between IoT devices. MP-NIKE schemes can be realized by using multilinear maps. There are several attempts for constructing multilinear maps based on indistinguishable obfuscation, lattices and the Chinese Remainder Theorem (CRT). Nevertheless, these schemes are inefficient in terms of computation cost and memory overhead. Besides, several attacks have been recently reported against CRT-based and lattice-based multilinear maps. There is only one modular exponentiation-based MP-NIKE scheme in the literature which has been claimed to be both secure and efficient. In this article, we present an attack on this scheme based on the Euclidean algorithm, in which two colluding users can obtain the shared key of any arbitrary subgroup of users. We also propose an efficient and secure MP-NIKE scheme. We show how our proposal is secure in the random oracle model assuming the hardness of the root extraction modulo a composite number. INDEX TERMS Multi-party non-interactive key exchange, broadcast encryption, Internet of Things, random oracle model.

Efficient Multilinear Map from Graded Encoding Scheme

“…An MP-NIKE scheme without key generation algorithm run by TTP is proposed in Section 5. In Section 6, the MP-NIKE scheme of [1] is converted to an ID-Based scheme. The security of the proposed multilinear map is proved in Section 7, and finally, the paper is concluded in Section 2.…”

“…In ID-based cryptography, the public key of users is obtained directly from the identity of users. Fortunately, in the MP-NIKE scheme of [1] any logN -bit random integer r can be a valid public key and the KGC has a trapdoor to compute its respective private key, while others cannot do it. The TTP can use algorithm ID-KeyGen(SP, ID i ) to compute the private key of user i.…”

“…by linear combination of p and xq [25]. So, any n-bit random integer r can be valid public key of MP-NIKE scheme of [1].…”

“…The security of this proposed GES scheme is proved in this Section. First, in Theorem 2, the intractability of decompositioning an encoding u = [r] 1 to e 1 r (1)…”

“…This new GES provides the actual functionality of the usual GES and can be applied in constructing a secure and efficient multilinear map and a multi-party non-interactive key exchange (MP-NIKE) scheme. We also improve the MP-NIKE scheme of [1] and turn it into an ID-based MP-NIKE scheme.…”