Abstract
A set operation problem is considered in the secure computation setting. Player A has a secret set SA and player B has a secret set SB,where SA and SB belong to a universe. They want to know if SA includes SB without leaking anything else about their secret sets. Three protocols of different levels of security and efficiency are proposed for this problem. The first protocol can be based on the so-called Superposed Encryption scheme or threshold encryption scheme. Let NB be the size of set SB,the first protocol needs NB rounds of communication. The other two protocols are based on standard public-key encryption schemes with additively homomorphic property,and need only one round of communication. Compared to previous results,the first two protocols use a new technique of representing sets,and the third protocol avoids threshold decryption in the output phase,and is more efficient.
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