Paper 2022/441
TwoClient InnerProduct Functional Encryption, with an Application to MoneyLaundering Detection
Abstract
In this paper, we extend InnerProduct Functional Encryption (IPFE), where there is just a vector in the key and a vector in the single sender's ciphertext, to twoclient ciphertexts. More precisely, in our twoclient functional encryption scheme, there are two data providers who can independently encrypt vectors $\mathbf{x}$ and $\mathbf{y}$ for a data consumer who can, from a functional decryption key associated to a vector $\mathbf{\alpha}$, compute $\sum \alpha_i x_i y_i = \mathbf{x} \cdot \mathsf{Diag}(\mathbf{\alpha}) \cdot \mathbf{y}^\top$. Ciphertexts are linear in the dimension of the vectors, whereas the functional decryption keys are of constant size. We study two interesting particular cases:  2party InnerProduct Functional Encryption, with $\mathbf{\alpha}= (1,\ldots,1)$. There is a unique functional decryption key, which enables the computation of $\mathbf{x}\cdot \mathbf{y}^\top$ by a third party, where $\mathbf{x}$ and $\mathbf{y}$ are provided by two independent clients;  InnerProduct Functional Encryption with a Selector, with $\mathbf{x}= \mathbf{x}_0 \ \mathbf{x}_1$ and $\mathbf{y}= \bar{b}^n \ b^n \in \{ 1^n \ 0^n, 0^n \ 1^n \}$, for some bit $b$, on the public coefficients $\mathbf{\alpha} = \mathbf{\alpha}_0 \ \mathbf{\alpha}_1$, in the functional decryption key, so that one gets $\mathbf{x}_b \cdot \mathbf{\alpha}_b^\top$, where $\mathbf{x}$ and $b$ are provided by two independent clients. This result is based on the fundamental ProductPreserving Lemma, which is of independent interest. It exploits Dual Pairing Vector Spaces (DPVS), with security proofs under the $\mathsf{SXDH}$ assumption. We provide two practical applications: to medical diagnosis for the latter IPFE with Selector, and to moneylaundering detection for the former 2party IPFE, both with strong privacy properties, with adaptative security and the use of labels granting a MultiClient Functional Encryption (MCFE) security for the scheme, thus enabling its use in practical situations.
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 Preprint.
 Keywords
 MCFE IPFE QFE Functional Encryption Dual Pairing Vector Bases MultiClient Money Laundering Detection Selector
 Contact author(s)

paola de perthuis @ ens fr
david pointcehval @ ens fr  History
 20220609: revised
 20220412: received
 See all versions
 Short URL
 https://ia.cr/2022/441
 License

CC BY
BibTeX
@misc{cryptoeprint:2022/441, author = {Paola de Perthuis and David Pointcheval}, title = {TwoClient InnerProduct Functional Encryption, with an Application to MoneyLaundering Detection}, howpublished = {Cryptology ePrint Archive, Paper 2022/441}, year = {2022}, note = {\url{https://eprint.iacr.org/2022/441}}, url = {https://eprint.iacr.org/2022/441} }