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Paper   IPM / M / 17252
School of Mathematics
  Title:   Flexible multi-client functional encryption for set intersection
  Author(s):  Mojtaba Rafiee
  Status:   Published
  Journal: The Journal of Supercomputing
  Year:  2023
  Pages:   DOI: 10.1007/s11227-023-05129-y
  Supported by:  IPM
A multi-client functional encryption (𝖬𝖢𝖥𝖤) scheme [Goldwasser–Gordon–Goyal 2014] for set intersection is a cryptographic primitive that enables an evaluator to learn the intersection from all sets of a predetermined number of clients, without need to learn the plaintext set of each individual client. Using these schemes, it is impossible to compute the set intersections from arbitrary subsets of clients, and thus, this constraint limits the range of its applications. To provide such a possibility, we redefine the syntax and security notions of 𝖬𝖢𝖥𝖤 schemes, and introduce flexible multi-client functional encryption (𝖥𝖬𝖢𝖥𝖤) schemes. We extend the 𝖺𝖨𝖭𝖣 security of 𝖬𝖢𝖥𝖤 schemes to 𝖺𝖨𝖭𝖣 security of 𝖥𝖬𝖢𝖥𝖤 schemes in a straightforward way. For a universal set with polynomial size in security parameter, we propose an 𝖥𝖬𝖢𝖥𝖤 construction for achieving 𝖺𝖨𝖭𝖣 security. Our construction computes set intersection for n clients that each holds a set with m elements, in time O(𝑛𝑚). We also prove the security of our construction under DDH1 that it is a variant of the symmetric external Diffie–Hellman (SXDH) assumption.

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