Three-Party Integer Comparison and Applications

Privacy-Preserving Closest Point Determination Based on Ciphertext Comparison

“…The comparison of distances can be completed through integer comparison schemes. Damgård et al [15] and Ma et al [19] both proposed integer comparison schemes when studying online auction applications. In [15], the two-party integer comparison protocol based on an additively homomorphic encryption system could compare one bit each time, which took at least log 2 M bit-by-bit homomorphic operations, where M was the upper bound of the integer to be compared.…”

“…In [15], the two-party integer comparison protocol based on an additively homomorphic encryption system could compare one bit each time, which took at least log 2 M bit-by-bit homomorphic operations, where M was the upper bound of the integer to be compared. However, many comparison schemes could directly compare small integers, such as [16], [18], [19]. Carlton et al [16] proposed a two-party integer comparison protocol, which has a per-bit comparison up to five times faster than [15] but required more interactions.…”

“…However, the upper bound of integers to be compared is smaller than others and the protocol was secure only in the Random-oracle (RO) model. In [19], a three-party integer comparison protocol using three homomorphic encryption systems was proposed, whose computational and communication complexity are higher.…”

“…We now compare our three-party integer comparison protocol Π TICP with other protocols [16], [18], [19]. Each of the four protocols can directly compare small integers.…”

“…In conclusion, there are two functionalities to be implemented: confidential calculation and comparison of distances, both of which can be completed using partially homomorphic encryption systems. For example, the distance could be calculated directly in ciphertext [10]- [14] and the integer comparison scheme based homomorphic encryption [15]- [19] can be used for the comparison of distance. In the following, we review the current studies and point out why they cannot fully address the "three-party PPCPD" challenge.…”