Recently, as also referred to as the cloud era, for various personal data set that perform machine learning analyzed it has become common. Order to prepare a personal data set that can withstand the analysis only one enterprise is often difficult, is expected to create detailed personal data set by combining data of several companies. However, since the personal data is personal information must be handled while protecting the privacy, it is impossible to carry out such operations in a conventional communication method. Therefore the protocol devised to solve this problem is PSI. Private Set Intersection performs operation into two or more secrets set the Protocol, but to output the result, it is necessary to communicate the elements of the set to the other secret held by their in the process. The primitive methods is a method of transmitting by encrypting each individual element of the secret set, since the process of the arithmetic and it is this method becomes complicated, other data representations easily perform arithmetic secret collection that you fix in it is considered. One of the scheme is the Bloom Filter. The sequence initial value is 0, one prepared a number of through each element of the secret set to the hash function, and stores information of all the elements by one of the elements of the sequence corresponding to the output to the first array to. This method can also accommodate complex operations such as derivation of the set of even small amount of communication, also occurs more than a certain number of times the union by utilizing the extended method such Comparable Bloom Filter element (Reduction). However, it is not possible to hold the information when has entered more than once the same elements in the secret set. There is also a method called polynomial representation using a polynomial to the solution of each element of the secret set, it is possible to Bloom Filter as well as the number of elements and Reduction of the derivation of the product set not only the product set. But subject to encrypt the transmission is a coefficient of the polynomial, the communication amount increases compared with Bloom Filter to a value over a finite field. This way there are various schemes for PSI, both of which are advantages and disadvantages. Its presence for unified approach is expected, detailed study of each technique has a very important meaning in the development of PSI. PSI each of the players to output the input and the product set a secret set of possession, but it is not possible to each player to obtain any information other than the product set at that time. Therefore, even by using the PSI to the communication between the personal data set and not the privacy of personal data is compromised. Once PSI but could only derivation of the product set, now has appeared even more complex than PSI, etc. to derive only the number of elements in the product set. Therefore, the role PSI research plays in data communications has also been increasing, the present study if realize high-speed PSI is believed to contribute significantly to secure data communications in consideration of the more privacy.