  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.
