- Can the rate of the construction by Choi et al. of NM-CPA from IND-CPA be improved?
- Is it possible to achieve multi-bit NM-CPA security more efficiently from a single-bit NM-CPA scheme than from IND-CPA?
- Is there a notion stronger than NM-CPA that has natural applications and can be achieved from IND-CPA security?
We answer all three questions in the positive. First, we improve the rate in the construction of Choi et al. by a factor O(k), where k is the security parameter. Still, encrypting a message of size O(k) would require ciphertext and keys of size O(k^2) times that of the IND-CPA scheme, even in our improved scheme. Therefore, we show a more efficient domain extension technique for building a k-bit NM-CPA scheme from a single-bit NM-CPA scheme with keys and ciphertext of size O(k) times that of the NM-CPA one-bit scheme. To achieve our goal, we define and construct a novel type of continuous non-malleable code (NMC), called secret-state NMC, as we show that standard continuous NMCs are not enough for the natural "encode-then-encrypt-bit-by-bit" approach to work.
Finally, we introduce a new security notion for public-key encryption (PKE) that we dub non-malleability under (chosen-ciphertext) self-destruct attacks (NM-SDA). After showing that NM-SDA is a strict strengthening of NM-CPA and allows for more applications, we nevertheless show that both of our results---(faster) construction from IND-CPA and domain extension from one-bit scheme---also hold for our stronger NM-SDA security. In particular, the notions of IND-CPA, NM-CPA, and NM-SDA security are all equivalent, lying (plausibly, strictly?) below IND-CCA security.Category / Keywords: public-key cryptography / Non-Malleable Codes, Public-Key Encryption, Non-Malleable Encryption Date: received 3 Aug 2015, last revised 5 Aug 2015 Contact author: corettis at inf ethz ch Available format(s): PDF | BibTeX Citation Version: 20150805:133420 (All versions of this report) Short URL: ia.cr/2015/772 Discussion forum: Show discussion | Start new discussion