Cryptology ePrint Archive: Report 2018/565

Homomorphic Encryption for Approximate Matrix Arithmetic

Jung Hee Cheon and Andrey Kim

Abstract: 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.

Category / Keywords: Homomorphic encryption, approximate arithmetic, matrix multiplication, matrix inverse, transposition

Date: received 27 May 2018, last revised 4 Jun 2018, withdrawn 9 Oct 2018

Contact author: kimandrik at snu ac kr

Available format(s): (-- withdrawn --)

Version: 20181010:041851 (All versions of this report)

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