Abstract: The most existing protocols for secure computation of set-inclusion are based on multiple public-key encryption algorithms and cannot either be computed publicly, which makes the computation complexity high and the application range limited as well. To cope with these problems, we design two protocols for secure computation of set-inclusion with the unencrypted method. Protocol 1 first transforms the original problem into the scalar-product problem, and then solves it with the hard problem in cryptography. Next, we present the practical protocol 2 under a certain scenario with a third untrusted party, in which we solve the set-inclusion problem combing the bilinear pairing with the hard problem in cryptography. Lastly, we give the security proof of two protocols, the performance analysis and comparison with others. Both of our protocols employ neither any public-key encryption algorithm nor multiple matching searches so as to avoid the intricate procedures of key-generation, encryption and decryption. This makes our protocols more efficient and concise than the previously known. In addition, we extend the secure computation of set-inclusion to a new application scenario, in which we can determine the set-inclusion relation publicly without revealing the privacy of both sets even if the untrusted third party exists.

Key words: set-inclusion, secure computation, bilinear pairing, hard mathematics problem, public determination