Paper 2016/432

Two-Input Functional Encryption for Inner Products from Bilinear Maps

Kwangsu Lee and Dong Hoon Lee


Functional encryption is a new paradigm of public-key encryption that allows a user to compute $f(x)$ on encrypted data $CT(x)$ with a private key $SK_f$ to finely control the revealed information. Multi-input functional encryption is an important extension of (single-input) functional encryption that allows the computation $f(x_1, \ldots, x_n)$ on multiple ciphertexts $CT(x_1), \ldots, CT(x_n)$ with a private key $SK_f$. Although multi-input functional encryption has many interesting applications like running SQL queries on encrypted database and computation on encrypted stream, current candidates are not yet practical since many of them are built on indistinguishability obfuscation. To solve this unsatisfactory situation, we show that practical two-input functional encryption schemes for inner products can be built based on bilinear maps. In this paper, we first propose a two-input functional encryption scheme for inner products in composite-order bilinear groups and prove its selective IND-security under simple assumptions. Next, we propose a two-client functional encryption scheme for inner products where each ciphertext can be associated with a time period and prove its selective IND-security. Furthermore, we show that our two-input functional encryption schemes in composite-order bilinear groups can be converted into schemes in prime-order asymmetric bilinear groups by using the asymmetric property of asymmetric bilinear groups.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. MINOR revision.IEICE Transactions on Fundamentals of Electronics
Functional encryptionMulti-input functional encryptionInner productBilinear maps.
Contact author(s)
kwangsu @ sejong ac kr
2019-05-07: last of 2 revisions
2016-05-02: received
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      author = {Kwangsu Lee and Dong Hoon Lee},
      title = {Two-Input Functional Encryption for Inner Products from Bilinear Maps},
      howpublished = {Cryptology ePrint Archive, Paper 2016/432},
      year = {2016},
      doi = {10.1587/transfun.E101.A.915},
      note = {\url{}},
      url = {}
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