Two-Client Inner-Product Functional Encryption with an Application to Money-Laundering Detection

Abstract

In this paper, we extend Inner-Product Functional Encryption (IPFE), where there is just a vector in the key and a vector in the single sender's ciphertext, to two-client ciphertexts. More precisely, in our two-client functional encryption scheme, there are two Data Providers who can independently encrypt vectors x and y for a data consumer who can, from a functional decryption key associated to a vector α, compute g'αi xiyi = x Diag(α) yT. Ciphertexts are linear in the dimension of the vectors, whereas the functional decryption keys are of constant size. We study two interesting particular cases: 2-party Inner-Product Functional Encryption, with α = (1,...,1). There is a unique functional decryption key, which enables the computation of x xT by a third party, where x and y are provided by two independent clients; Inner-Product Functional Encryption with a Selector, with x = x0 II x1 and y = bn II bn g{1n || 0n, 0n II 1n}, for some bit b, on the public coefficients α = α0 II α1, in the functional decryption key, so that one gets xb αbT, where x and b are provided by two independent clients. This result is based on the fundamental Product-Preserving Lemma, which is of independent interest. It exploits Dual Pairing Vector Spaces (DPVS), with security proofs under the SXDH assumption. We provide two practical applications to medical diagnosis for the latter IPFE with a selector, and to money-laundering detection for the former 2-party IPFE, both with strong privacy properties, adaptative security and the use of labels granting a Multi-Client Functional Encryption (MCFE) security for the scheme, thus enabling its use in practical situations.