This work undertakes a comprehensive (crypt)analysis of property preserving symmetric encryption on both these fronts. We observe that the quadratic residue based property used in their separation result is a special case of testing equality of one-bit messages, suggest a very simple and efficient deterministic encryption scheme for testing equality and show that the two security notions, find-then-guess and left-or-right, are tightly equivalent in this setting. On the other hand, the separation result easily generalizes for the equality property. So contextualized, we posit that the question of separation between security notions is property specific and subtler than what the authors envisaged; mandating further critical investigation. Next, we show that given a find-then-guess secure orthogonality preserving encryption of vectors of length 2n, there exists left-or-right secure orthogonality preserving encryption of vectors of length n, giving further evidence that find-then-guess is indeed a meaningful notion of security for property preserving encryption. Finally, we cryptanalyze the scheme for testing orthogonality. A simple distinguishing attack establishes that it is not even the weakest selective find-then-guess secure. Our main attack extracts out the subgroup elements used to mask the message vector and indicates greater vulnerabilities in the construction beyond indistinguishability. Overall, our work underlines the importance of cryptanalysis in provable security.
Category / Keywords: bilinear pairings, property preserving encryption, predicate private encryption, symmetric key Date: received 3 Dec 2013, last revised 16 Sep 2015 Contact author: prem lax at gmail com Available format(s): PDF | BibTeX Citation Note: Major Revision Version: 20150917:013621 (All versions of this report) Short URL: ia.cr/2013/830 Discussion forum: Show discussion | Start new discussion