Homomorphic Encryption for Approximate Matrix Arithmetic

Homomorphic Encryption for Arithmetic of Approximate Numbers (HEAAN) with its vector packing technique proved its potential in cryptographic applications. In this paper, we propose MHEAAN a generalization of the HEAAN scheme to a multivariate case. Our design takes advantage of the HEAAN scheme, that the precision losses during the evaluation are limited by the depth of the circuit, and it exceeds no more than one bit compared to unencrypted approximate arithmetic, such as floating point operations. In addition, with a multivariate structure of the plaintext space, we suggest a general method of packing multidimensional structures as matrices and tensors in a single ciphertext. We provide a concrete two-dimensional construction and show the efficiency of our scheme on several matrix operations, such as matrix transposition, matrix multiplication, and inverse.

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