  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.
