An Efficient Secure Integer Comparison Protocol Via Private Set Intersection

Secure integer comparison is a basic computing function in many applications, such as online auctions, data mining, etc. In a two-party comparison scenario, Alice and Bob hold two private integers <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y$</tex> respectively. One of them can obtain the comparison result, without leaking any other information of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y$</tex> to each other. At present, there have some methods to solve this problem. Most solutions decompose integers into bitwise representations, and then encrypt each bit for secure comparison. However, this type of solution is expensive for large integer comparisons, because each bit needs to be encrypted and decrypted. In this paper, 0/1 encoding is used to convert integers into binary bit strings and compare them with private set intersection technology. Only a small amount of encryption is needed to perform secure integer comparison, and we apply the protocol to the machine learning decision tree scenario, which can ensure that the final classification result is output correctly without leaking any private data. The results show that our proposed solution has obvious computational efficiency advantages when comparing large integers, and can be applied to more application scenarios.