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

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 secret sharing against joint tampering attacks

Since thousands of years ago, the goal of cryptography has been to hide messages from prying eyes. In recent times, cryptography two important changes: first, cryptography itself evolved from just being about encryption to a broader class of situations coming from the digital era; second, the way of studying cryptography evolved from creating ``seemingly hard'' cryptographic schemes to constructing schemes which are provably secure. However, once the mathematical abstraction of cryptographic primitives started to be too hard to break, attackers found another way to defeat security. Side channel attacks have been proved to be very effective in this task, breaking the security of otherwise provably secure schemes. Because of this, recent trends in cryptography aim to capture this situation and construct schemes that are secure even against such powerful attacks. In this setting, this thesis specializes in the study of secret sharing, an important cryptographic primitive that allows to balance privacy and integrity of data and also has applications to multi-party protocols. Namely, continuing the trend which aims to protect against side channel attacks, this thesis brings some contributions to the state of the art of the so-called leakage-resilient and non-malleable secret sharing schemes, which have stronger guarantees against attackers that are able to learn information from possibly all the shares and even tamper with the shares and see the effects of the tampering. The main contributions of this thesis are twofold. First, we construct secret sharing schemes that are secure against a very powerful class of attacks which, informally, allows the attacker to jointly leak some information and tamper with the shares in a continuous fashion. Second, we study the capacity of continuously non-malleable secret sharing schemes, that is, the maximum achievable information rate. Roughly speaking, we find some lower bounds to the size that the shares must have in order to achieve some forms of non-malleability

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

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

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

Bounded Tamper Resilience: How to go beyond the Algebraic Barrier

Related key attacks (RKAs) are powerful cryptanalytic attacks where an adversary can change the secret key and observe the effect of such changes at the output. The state of the art in RKA security protects against an a-priori unbounded number of certain algebraic induced key relations, e.g., affine functions or polynomials of bounded degree. In this work, we show that it is possible to go beyond the algebraic barrier and achieve security against arbitrary key relations, by restricting the number of tampering queries the adversary is allowed to ask for. The latter restriction is necessary in case of arbitrary key relations, as otherwise a generic attack of Gennaro et al. (TCC 2004) shows how to recover the key of almost any cryptographic primitive. We describe our contributions in more detail below. 1) We show that standard ID and signature schemes constructed from a large class of $\Sigma$-protocols (including the Okamoto scheme, for instance) are secure even if the adversary can arbitrarily tamper with the prover’s state a bounded number of times and obtain some bounded amount of leakage. Interestingly, for the Okamoto scheme we can allow also independent tampering with the public parameters. 2) We show a bounded tamper and leakage resilient CCA secure public key cryptosystem based on the DDH assumption. We first define a weaker CPA-like security notion that we can instantiate based on DDH, and then we give a general compiler that yields CCA-security with tamper and leakage resilience. This requires a public tamper-proof common reference string. 3) Finally, we explain how to boost bounded tampering and leakage resilience (as in 1. and 2. above) to continuous tampering and leakage resilience, in the so-called floppy model where each user has a personal hardware token (containing leak- and tamper-free information) which can be used to refresh the secret key. We believe that bounded tampering is a meaningful and interesting alternative to avoid known impossibility results and can provide important insights into the security of existing standard cryptographic schemes

Strong Continuous Non-malleable Encoding Schemes with Tamper-Detection

A non-malleable encoding scheme is a keyless encoding scheme which is resilient to tampering attacks. Such a scheme is said to be continuously secure if the scheme is resilient to attacks containing more than one tampering procedure. Also, such a scheme is said to have tamper-detection property if any kind of tampering attack is detected. In [S. Faust, et al., Continuous nonmalleable codes, TCC Proc., LNCS Vol. 8349, 2014.] a general continuous non-malleable encoding scheme based on NIZK is introduced which is secure in a strong model for which the adversary receives a no-tamper as a response to its tampering query if the decoding of the tampered codeword is identical to the original message. In this article we introduce a new strongly secure continuous non-malleable encoding scheme with tamper-detection property whose security is based on the existence of secure MAC’s. Moreover, we introduce and justify the importance of an intermediate security model called semi-strong continuous non-malleability, while we provide a secure semi-strong continuous non-malleable encoding scheme whose security is based on the existence of CCA-secure public-key encryption. Considering the area of applications of encoding schemes in tamper-proof devices, it is instructive to note that our proposed schemes can be used to implement an algorithmic tamperdetection level as well as maintaining the security conditions

Public Key Encryption Resilient to Post-Challenge Leakage and Tampering Attacks

In this paper, we introduce a new framework for constructing public-key encryption (PKE) schemes resilient to joint post-challenge/after-the-fact leakage and tampering attacks in the bounded leakage and tampering (BLT) model, introduced by Damgård et al. (Asiacrypt 2013). All the prior formulations of PKE schemes considered leakage and tampering attacks only before the challenge ciphertext is made available to the adversary. However, this restriction seems necessary, since achieving security against post-challenge leakage and tampering attacks in its full generality is impossible as shown in previous works. In this paper, we study the post-challenge/after-the-fact security for PKE schemes against bounded leakage and tampering under a restricted yet meaningful and reasonable notion of security, namely, the split-state leakage and tampering model. We show that it is possible to construct secure PKE schemes in this model, tolerating arbitrary (but bounded) leakage and tampering queries; thus overcoming the previous impossibility results. To this end, we formulate a new notion of security, which we call entropic post-challenge IND-CCA-BLT secure PKE. We first define a weaker notion called entropic restricted post-challenge IND-CCA-BLT secure PKE, which can be instantiated using the (standard) DDH assumption. We then show a generic compiler from our entropic restricted notion to the entropic notion of security using a simulation-extractable non-interactive zero-knowledge argument system. This requires an untamperable common reference string as in previous works. Finally, we demonstrate the usefulness of our entropic notion of security by giving a simple and generic construction of post-challenge IND-CCA-BLT secure PKE scheme in the split-state leakage and tampering model. This also settles the open problem posed by Faonio and Venturi (Asiacrypt 2016)

Impossibility on Tamper-Resilient Cryptography with Uniqueness Properties

In this work, we show negative results on the tamper-resilience of a wide class of cryptographic primitives with uniqueness properties, such as unique signatures, verifiable random functions, signatures with unique keys, injective one-way functions, and encryption schemes with a property we call unique-message property. Concretely, we prove that for these primitives, it is impossible to derive their (even extremely weak) tamper-resilience from any common assumption, via black-box reductions. Our proofs exploit the simulatable attack paradigm proposed by Wichs (ITCS ’13), and the tampering model we treat is the plain model, where there is no trusted setup