Abstract
In a seminal paper, Dolev
et al. [
15] introduced the notion of
non-malleable encryption (NM-CPA). This notion is very intriguing since it suffices for many applications of chosen-ciphertext secure encryption (IND-CCA), and, yet, can be generically built from semantically secure (IND-CPA) encryption, as was shown in the seminal works by Pass
et al. [
29] and by Choi
et al. [
9], the latter of which provided a black-box construction. In this paper we investigate three questions related to NM-CPA security:
1.
Can the rate of the construction by Choi et al. of NM-CPA from IND-CPA be improved?
2.
Is it possible to achieve multi-bit NM-CPA security more efficiently from a single-bit NM-CPA scheme than from IND-CPA?
3.
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 scheme of Choi et al. by a factor \(\mathcal {O}(\lambda )\), where \(\lambda \) is the security parameter. Still, encrypting a message of size \(\mathcal {O}(\lambda )\) would require ciphertext and keys of size \(\mathcal {O}(\lambda ^2)\) times that of the IND-CPA scheme, even in our improved scheme. Therefore, we show a more efficient domain extension technique for building a \(\lambda \)-bit NM-CPA scheme from a single-bit NM-CPA scheme with keys and ciphertext of size \(\mathcal {O}(\lambda )\) 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 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.