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A stochastic number representation for fully homomorphic cryptography

Privacy of data has become an increasing concern over the past years. With Fully Homomorphic Encryption (FHE), one can offload the processing of data to a third-party while keeping it private. A technique called batching has been proposed to accelerate FHE, allowing for several bits to be encrypted in the same ciphertext, which can be processed in parallel. Herein, we argue that for a certain class of applications, a stochastic representation of numbers takes optimal advantage of this technique. Operations on stochastic numbers have direct homomorphic counterparts, leading to low degree arithmetic circuits for the evaluation of additions and multiplications. Moreover, an efficient technique for the homomorphic evaluation of nonlinear functions is proposed in this paper. The applicability of the proposed methods is assessed with efficient and accurate proof-of-concept implementations of homomorphic image processing, as well as the homomorphic evaluation of radial basis functions for Support Vector Machines (SVMs).