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)

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

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

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

Cryptographic techniques for hardware security

Traditionally, cryptographic algorithms are designed under the so-called black-box model, which considers adversaries that receive black-box access to the hardware implementation. Although a "black-box" treatment covers a wide range of attacks, it fails to capture reality adequately, as real-world adversaries can exploit physical properties of the implementation, mounting attacks that enable unexpected, non-black-box access, to the components of the cryptographic system. This type of attacks is widely known as physical attacks, and has proven to be a significant threat to the real-world security of cryptographic systems. The present dissertation is (partially) dealing with the problem of protecting cryptographic memory against physical attacks, via the use of non-malleable codes, which is a notion introduced in a preceding work, aiming to provide privacy of the encoded data, in the presence of adversarial faults. In the present thesis we improve the current state-of-the-art on non-malleable codes and we provide practical solutions for protecting real-world cryptographic implementations against physical attacks. Our study is primarily focusing on the following adversarial models: (i) the extensively studied split-state model, which assumes that private memory splits into two parts, and the adversary tampers with each part, independently, and (ii) the model of partial functions, which is introduced by the current thesis, and models adversaries that access arbitrary subsets of codeword locations, with bounded cardinality. Our study is comprehensive, covering one-time and continuous, attacks, while for the case of partial functions, we manage to achieve a stronger notion of security, that we call non-malleability with manipulation detection, that in addition to privacy, it also guarantees integrity of the private data. It should be noted that, our techniques are also useful for the problem of establishing, private, keyless communication, over adversarial communication channels. Besides physical attacks, another important concern related to cryptographic hardware security, is that the hardware fabrication process is assumed to be trusted. In reality though, when aiming to minimize the production costs, or whenever access to leading-edge manufacturing facilities is required, the fabrication process requires the involvement of several, potentially malicious, facilities. Consequently, cryptographic hardware is susceptible to the so-called hardware Trojans, which are hardware components that are maliciously implanted to the original circuitry, having as a purpose to alter the device's functionality, while remaining undetected. Part of the present dissertation, deals with the problem of protecting cryptographic hardware against Trojan injection attacks, by (i) proposing a formal model for assessing the security of cryptographic hardware, whose production has been partially outsourced to a set of untrusted, and possibly malicious, manufacturers, and (ii) by proposing a compiler that transforms any cryptographic circuit, into another, that can be securely outsourced

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

Unbounded Leakage-Resilience and Leakage-Detection in a Quantum World

Side-channel attacks, which aim to leak side information on secret system components, are ubiquitous. Even simple attacks, such as measuring time elapsed or radiation emitted during encryption and decryption procedures, completely break textbook versions of many cryptographic schemes. This has prompted the study of leakage-resilient cryptography, which remains secure in the presence of side-channel attacks. Classical leakage-resilient cryptography must necessarily impose restrictions on the type of leakage one aims to protect against. As a notable example, the most well-studied leakage model is that of bounded leakage, where it is assumed that an adversary learns at most $\ell$ bits of leakage on secret components, for some leakage bound $\ell$. Although this leakage bound is necessary, it is unclear if such a bound is realistic in practice since many practical side-channel attacks cannot be captured by bounded leakage. In this work, we investigate the possibility of designing cryptographic schemes that provide guarantees against arbitrary side-channel attacks: - Using techniques from uncloneable quantum cryptography, we design several basic leakage-resilient primitives, such as secret sharing, (weak) pseudorandom functions, digital signatures, and public- and private-key encryption, which remain secure under (polynomially) unbounded classical leakage. In particular, this leakage can be much longer than the (quantum) secret being leaked upon. In our view, leakage is the result of observations of quantities such as power consumption and hence is most naturally viewed as classical information. - In the even stronger adversarial setting where the adversary is allowed to obtain unbounded quantum leakage (and thus leakage-resilience is impossible), we design schemes for many cryptographic tasks which support leakage-detection. This means that we can efficiently check whether the security of such a scheme has been compromised by a side-channel attack. These schemes are based on techniques from cryptography with certified deletion. - We also initiate a study of classical cryptographic schemes with (bounded) post-quantum leakage-resilience. These schemes resist side-channel attacks performed by adversaries with quantum capabilities which may even share arbitrary entangled quantum states. That is, even if such adversaries are non-communicating, they can still have spooky communication via entangled states