Fast but approximate homomorphic k-means based on masking technique

Abstract

AbstractNowadays, computing on encrypted data seems to be more practical than a few years ago, thanks to the emergence of new Homomorphic Encryption schemes. In this paper, an algorithm based on Homomorphic Encryption for Arithmetic of Approximate Numbers (Cheon et al., in: Takagi, Peyrin (eds) Advances in cryptology—ASIACRYPT 2017, Springer, Cham, pp 409–437, 2017) (HEAAN, or also CKKS) scheme, that is able to perform a secure k-means algorithm which processes encrypted data, has been studied and presented. The performance of the classifier running on encrypted data has been evaluated using a standard k-means algorithm that works on plain data as a supervised structure, since the results are obtained by approximated computations. The main point of this paper is to take existent theoretical techniques (for example approximations of $$\text {sgn}(x)$$ sgn ( x ) ), to use them and to observe if they are valid in practical applications. The output of the algorithm is a set of k encrypted masks that can be applied to the original dataset in order to obtain different clusters. The setting is a standard client–server one. The workload is heavily server-centric, as the client only has to execute a light masking algorithm at the end of each iteration, which, excluding the decryption, is faster than a plain k-means iteration; the main disadvantage concerns the accuracy of the results. Experiments show that the algorithm can be executed fairly quickly: the execution time of the training phase is on the order of seconds, while classification is on the order of tenths of a second.