Non-malleable encryption: simpler, shorter, stronger

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 O(λ), where λ is the security parameter. Still, encrypting a message of size O(λ) would require ciphertext and keys of size O(λ2) times that of the IND-CPA scheme, even in our improved scheme. Therefore, we show a more efficient domain extension technique for building a λ-bit NM-CPA scheme from a single-bit NM-CPA scheme with keys and ciphertext of size O(λ) 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 securit

Continuously non-malleable codes with split-state refresh

Non-malleable codes for the split-state model allow to encode a message into two parts, such that arbitrary independent tampering on each part, and subsequent decoding of the corresponding modified codeword, yields either the same as the original message, or a completely unrelated value. Continuously non-malleable codes further allow to tolerate an unbounded (polynomial) number of tampering attempts, until a decoding error happens. The drawback is that, after an error happens, the system must self-destruct and stop working, otherwise generic attacks become possible. In this paper we propose a solution to this limitation, by leveraging a split-state refreshing procedure. Namely, whenever a decoding error happens, the two parts of an encoding can be locally refreshed (i.e., without any interaction), which allows to avoid the self-destruct mechanism. An additional feature of our security model is that it captures directly security against continual leakage attacks. We give an abstract framework for building such codes in the common reference string model, and provide a concrete instantiation based on the external Diffie-Hellman assumption. Finally, we explore applications in which our notion turns out to be essential. The first application is a signature scheme tolerating an arbitrary polynomial number of split-state tampering attempts, without requiring a self-destruct capability, and in a model where refreshing of the memory happens only after an invalid output is produced. This circumvents an impossibility result from a recent work by Fuijisaki and Xagawa (Asiacrypt 2016). The second application is a compiler for tamper-resilient RAM programs. In comparison to other tamper-resilient compilers, ours has several advantages, among which the fact that, for the first time, it does not rely on the self-destruct feature

Non-Malleable Codes for Small-Depth Circuits

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e. $\mathsf{AC^0}$ tampering functions), our codes have codeword length $n = k^{1+o(1)}$ for a $k$-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay and Li (STOC 2017), which had codeword length $2^{O(\sqrt{k})}$. Our construction remains efficient for circuit depths as large as $\Theta(\log(n)/\log\log(n))$ (indeed, our codeword length remains $n\leq k^{1+\epsilon})$, and extending our result beyond this would require separating $\mathsf{P}$ from $\mathsf{NC^1}$. We obtain our codes via a new efficient non-malleable reduction from small-depth tampering to split-state tampering. A novel aspect of our work is the incorporation of techniques from unconditional derandomization into the framework of non-malleable reductions. In particular, a key ingredient in our analysis is a recent pseudorandom switching lemma of Trevisan and Xue (CCC 2013), a derandomization of the influential switching lemma from circuit complexity; the randomness-efficiency of this switching lemma translates into the rate-efficiency of our codes via our non-malleable reduction.Comment: 26 pages, 4 figure

Predictable arguments of knowledge

We initiate a formal investigation on the power of predictability for argument of knowledge systems for NP. Specifically, we consider private-coin argument systems where the answer of the prover can be predicted, given the private randomness of the verifier; we call such protocols Predictable Arguments of Knowledge (PAoK). Our study encompasses a full characterization of PAoK, showing that such arguments can be made extremely laconic, with the prover sending a single bit, and assumed to have only one round (i.e., two messages) of communication without loss of generality. We additionally explore PAoK satisfying additional properties (including zero-knowledge and the possibility of re-using the same challenge across multiple executions with the prover), present several constructions of PAoK relying on different cryptographic tools, and discuss applications to cryptography

The chaining lemma and its application

We present a new information-theoretic result which we call the Chaining Lemma. It considers a so-called “chain” of random variables, defined by a source distribution X(0)with high min-entropy and a number (say, t in total) of arbitrary functions (T1,…, Tt) which are applied in succession to that source to generate the chain (Formula presented). Intuitively, the Chaining Lemma guarantees that, if the chain is not too long, then either (i) the entire chain is “highly random”, in that every variable has high min-entropy; or (ii) it is possible to find a point j (1 ≤ j ≤ t) in the chain such that, conditioned on the end of the chain i.e. (Formula presented), the preceding part (Formula presented) remains highly random. We think this is an interesting information-theoretic result which is intuitive but nevertheless requires rigorous case-analysis to prove. We believe that the above lemma will find applications in cryptography. We give an example of this, namely we show an application of the lemma to protect essentially any cryptographic scheme against memory tampering attacks. We allow several tampering requests, the tampering functions can be arbitrary, however, they must be chosen from a bounded size set of functions that is fixed a prior

A Tamper and Leakage Resilient von Neumann Architecture

We present a universal framework for tamper and leakage resilient computation on a von Neumann Random Access Architecture (RAM in short). The RAM has one CPU that accesses a storage, which we call the disk. The disk is subject to leakage and tampering. So is the bus connecting the CPU to the disk. We assume that the CPU is leakage and tamper-free. For a fixed value of the security parameter, the CPU has constant size. Therefore the code of the program to be executed is stored on the disk, i.e., we consider a von Neumann architecture. The most prominent consequence of this is that the code of the program executed will be subject to tampering. We construct a compiler for this architecture which transforms any keyed primitive into a RAM program where the key is encoded and stored on the disk along with the program to evaluate the primitive on that key. Our compiler only assumes the existence of a so-called continuous non-malleable code, and it only needs black-box access to such a code. No further (cryptographic) assumptions are needed. This in particular means that given an information theoretic code, the overall construction is information theoretic secure. Although it is required that the CPU is tamper and leakage proof, its design is independent of the actual primitive being computed and its internal storage is non-persistent, i.e., all secret registers are reset between invocations. Hence, our result can be interpreted as reducing the problem of shielding arbitrary complex computations to protecting a single, simple yet universal component

Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack

Efficient non-malleable codes and key derivation for poly-size tampering circuits

Non-malleable codes, defined by Dziembowski, Pietrzak, and Wichs (ICS '10), provide roughly the following guarantee: if a codeword c encoding some message x is tampered to c' = f(c) such that c' ≠ c , then the tampered message x' contained in c' reveals no information about x. The non-malleable codes have applications to immunizing cryptosystems against tampering attacks and related-key attacks. One cannot have an efficient non-malleable code that protects against all efficient tampering functions f. However, in this paper we show 'the next best thing': for any polynomial bound s given a-priori, there is an efficient non-malleable code that protects against all tampering functions f computable by a circuit of size s. More generally, for any family of tampering functions F of size F ≤ 2s , there is an efficient non-malleable code that protects against all f in F . The rate of our codes, defined as the ratio of message to codeword size, approaches 1. Our results are information-theoretic and our main proof technique relies on a careful probabilistic method argument using limited independence. As a result, we get an efficiently samplable family of efficient codes, such that a random member of the family is non-malleable with overwhelming probability. Alternatively, we can view the result as providing an efficient non-malleable code in the 'common reference string' model. We also introduce a new notion of non-malleable key derivation, which uses randomness x to derive a secret key y = h(x) in such a way that, even if x is tampered to a different value x' = f(x) , the derived key y' = h(x') does not reveal any information about y. Our results for non-malleable key derivation are analogous to those for non-malleable codes. As a useful tool in our analysis, we rely on the notion of 'leakage-resilient storage' of Davì, Dziembowski, and Venturi (SCN '10), and, as a result of independent interest, we also significantly improve on the parameters of such schemes

Non-malleable codes for space-bounded tampering

Non-malleable codes—introduced by Dziembowski, Pietrzak and Wichs at ICS 2010—are key-less coding schemes in which mauling attempts to an encoding of a given message, w.r.t. some class of tampering adversaries, result in a decoded value that is either identical or unrelated to the original message. Such codes are very useful for protecting arbitrary cryptographic primitives against tampering attacks against the memory. Clearly, non-malleability is hopeless if the class of tampering adversaries includes the decoding and encoding algorithm. To circumvent this obstacle, the majority of past research focused on designing non-malleable codes for various tampering classes, albeit assuming that the adversary is unable to decode. Nonetheless, in many concrete settings, this assumption is not realistic

Continuously non-malleable codes with split-state refresh

Non-malleable codes for the split-state model allow to encode a message into two parts, such that arbitrary independent tampering on each part, and subsequent decoding of the corresponding modified codeword, yields either the same as the original message, or a completely unrelated value. Continuously non-malleable codes further allow to tolerate an unbounded (polynomial) number of tampering attempts, until a decoding error happens. The drawback is that, after an error happens, the system must self-destruct and stop working, otherwise generic attacks become possible. In this paper we propose a solution to this limitation, by leveraging a split-state refreshing procedure. Namely, whenever a decoding error happens, the two parts of an encoding can be locally refreshed (i.e., without any interaction), which allows to avoid the self-destruct mechanism in some applications. Additionally, the refreshing procedure can be exploited in order to obtain security against continual leakage attacks. We give an abstract framework for building refreshable continuously non-malleable codes in the common reference string model, and provide a concrete instantiation based on the external Diffie–Hellman assumption. Finally, we explore applications in which our notion turns out to be essential. The first application is a signature scheme tolerating an arbitrary polynomial number of split-state tampering attempts, without requiring a self-destruct capability, and in a model where refreshing of the memory happens only after an invalid output is produced. This circumvents an impossibility result from a recent work by Fujisaki and Xagawa (Asiacrypt 2016). The second application is a compiler for tamper-resilient read-only RAM programs. In comparison to other tamper-resilient RAM compilers, ours has several advantages, among which the fact that, in some cases, it does not rely on the self-destruct feature