- We show that monotonic, small universe KP-ABE (CP-ABE) with bounds on the size of attribute sets and span programs (or linear secret sharing matrix) can be converted into DSE. Furthermore, we show that DSE implies non-monotonic CP-ABE (and KP-ABE) with the same bounds on parameters. This implies that monotonic/non-monotonic KP/CP-ABE (with the bounds) and DSE are all equivalent in the sense that one implies another.
- We also show that if we start from KP-ABE without bounds on the size of span programs (but bounds on the size of attribute sets), we can obtain ABE for arithmetic span programs. The other direction is also shown: ABE for arithmetic span programs can be converted into KP-ABE. These results imply, somewhat surprisingly, KP-ABE without bounds on span program sizes is in fact equivalent to ABE for arithmetic span programs, which was thought to be more expressive or at least incomparable.
By applying these conversions to existing schemes, we obtain many non-trivial consequences. We obtain the first non-monotonic, large universe CP-ABE (that supports span programs) with constant-size ciphertexts, the first KP-ABE with constant-size private keys, the first (adaptively-secure, multi-use) ABE for arithmetic span programs with constant-size ciphertexts, and more. We also obtain the first attribute-based signature scheme that supports non-monotone span programs and achieves constant-size signatures via our techniques.Category / Keywords: Attribute-based encryption, doubly spatial encryption, generic conversion, constant-size ciphertexts, constant-size keys, arithmetic span programs Date: received 6 May 2015, last revised 13 Jul 2015 Contact author: yamada-shota at aist go jp Available format(s): PDF | BibTeX Citation Version: 20150713:130805 (All versions of this report) Short URL: ia.cr/2015/431 Discussion forum: Show discussion | Start new discussion