Statistical analysis of largescale data is useful as it enables the extraction of a large amount of information, despite its simplicity. Therefore, fusing and analyzing data from different security domains is an attractive and promising approach, unless it jeopardizes the privacy of the data in any security domain. In this study, we proposed the HEaaN-STAT toolkit that can efficiently fuse data from different domains to enable largescale statistical analysis while protecting data privacy. Moreover, we proposed an efficient inverse operation and a table lookup function for Cheon-Kim-Kim-Song (CKKS) encrypted data, as well as a data encoding method for counting encrypted data. Based on this, we proposed a method for generating a contingency table with a large number of cases and k-percentile for largescale data that is hundreds to thousands of times faster than the method proposed by Lu et al. in NDSS’17. The validity of the proposed toolkit was verified through practical use for business applications using real-world data.

Making deep neural networks available as a service introduces privacy problems, for which homomorphic encryption of both model and user data potentially offers the solution at the highest privacy level. However, the difficulty of operating on homomorphically encrypted data has hitherto limited the range of operations available and the depth of networks. We introduce an extended CKKS scheme MatHEAAN to provide efficient matrix representations and operations together with improved noise control. Using the MatHEAAN we developed a deep sequential model with a gated recurrent unit called MatHEGRU. We evaluated the proposed model using sequence modeling, regression, and classification of images and genome sequences. We show that the hidden states of the encrypted model, as well as the results, are consistent with a plaintext model.

In this study, we propose an efficient sorting method for encrypted data using fully homomorphic encryption (FHE). The proposed method extends the existing 2-way sorting method by applying the k-way sorting network for any prime k to reduce the depth in terms of comparison operation from O(log22n) to O(klogk2n), thereby improving performance for k slightly larger than 2, such as k=5. We apply this method to approximate FHE which is widely used due to its efficiency of homomorphic arithmetic operations. In order to build up the k-way sorting network, the k-sorter, which sorts k-numbers with a minimal comparison depth, is used as a building block. The approximate homomorphic comparison, which is the only type of comparison working on approximate FHE, cannot be used for the construction of the k-sorter as it is because the result of the comparison is not binary, unlike the comparison in conventional bit-wise FHEs. To overcome this problem, we propose an efficient k-sorter construction utilizing the features of approximate homomorphic comparison. Also, we propose an efficient construction of a k-way sorting network using cryptographic SIMD operations. To use the proposed method most efficiently, we propose an estimation formula that finds the appropriate k that is expected to reduce the total time cost when the parameters of the approximating comparisons and the performance of the operations provided by the approximate FHE are given. We also show the implementation results of the proposed method, and it shows that sorting 56= 15625 data using 5-way sorting network can be about 23.3% faster than sorting 214= 16384 data using 2-way.

As a method of privacy-preserving data analysis (PPDA), a fully homomorphic encryption (FHE) has been in the spotlight recently. Unfortunately, because many data analysis methods assume that the type of data is of real type, the FHE-based PPDA methods could not support the enough level of accuracy due to the nature of FHE that fixed-point real-number representation is supported easily. In this paper, we propose a new method to represent encrypted floating-point real numbers on top of FHE. The proposed method is designed to have analogous range and accuracy to 32-bit floating-point number in IEEE 754 representation. We propose a method to perform arithmetic operations and size comparison operations. The proposed method is designed using two different FHEs, HEAAN and TFHE. As a result, HEAAN is proven to be very efficient for arithmetic operations and TFHE is efficient in size comparison. This study is expected to contribute to practical use of FHE-based PPDA.

This study examines the ordered bucketization (OB) as a cryptographic object. In OB, plaintextspace is divided into p disjoint buckets, numbered from 1 to p, based on the order of the ranges that they cover. OB is quite useful in that a range query can be performed over encrypted data without the need to descrypt by attaching a bucket number to each ciphertext. Unfortunately, no research has been carried out on the security of OB in a cryptographic sense. This paper defines an encryption scheme with OB (EOB) and suggests a new security model for EOB, IND-OCPA-P, which assumes an adversary has reasonable power. Previous constructions proposed for efficient range queries were not secure in this model. Finally, an OB construction, in which the EOB implementation is secure on the IND-OCPA-P model, is proposed. In the proposed OB, p- 1 points are selected on the uniform distribution in the plaintext-space and the plaintext-space is divided based on the selected points. A bucket number is assigned to each divided range in ascending range order. With regard to the efficiency of a range query, the proposed OB guarantees reasonably good efficiency on range queries by showing that the distribution of a bucket size is not skewed.