Secure Statistical Analysis Using RLWE-Based Homomorphic Encryption

Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption

“…In this section, we briefly review the previous packing methods proposed by L a u t e r et al [5] and Y a s u d a et al [9], [10] over the SHE scheme described in the previous section.…”

“…After that, Y a s u d a et al [9] proposed a new packing method for secure multiple inner products, which can be applied to secure Hamming distance and pattern matching computations. While their packing method is efficient only for vectors with small size entries, they modified their method for large size entries [10]. Their modified method can be applied to secure statistical analysis such as covariance and correlation between two variables with integers of practical size.…”

“…In this paper, we propose several packing methods for secure matrix multiplication, using the idea of Y a s u d a et al's methods [9], [10]. More specifically, for matrices with binary entries, our method is based on [9], and for non-binary entries, it is based on [10].…”

“…In this paper, we propose several packing methods for secure matrix multiplication, using the idea of Y a s u d a et al's methods [9], [10]. More specifically, for matrices with binary entries, our method is based on [9], and for non-binary entries, it is based on [10]. Our main ingredient for packing a matrix A is to deploy the entries of A into a single polynomial by using the packing methods of [9], [10], and then encrypt the polynomial over the SHE scheme.…”

“…More specifically, for matrices with binary entries, our method is based on [9], and for non-binary entries, it is based on [10]. Our main ingredient for packing a matrix A is to deploy the entries of A into a single polynomial by using the packing methods of [9], [10], and then encrypt the polynomial over the SHE scheme. Our matrix packing method requires only one homomorphic multiplication over our packed ciphertexts for secure matrix multiplication.…”