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

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

Limits to Non-Malleability

There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question: When can we rule out the existence of a non-malleable code for a tampering class ?? First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes: - Functions that change d/2 symbols, where d is the distance of the code; - Functions where each input symbol affects only a single output symbol; - Functions where each of the n output bits is a function of n-log n input bits. Furthermore, we rule out constructions of non-malleable codes for certain classes ? via reductions to the assumption that a distributional problem is hard for ?, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P ? NC

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

Rate-Optimizing Compilers for Continuously Non-Malleable Codes

We study the *rate* of so-called *continuously* non-malleable codes, which allow to encode a message in such a way that (possibly adaptive) continuous tampering attacks on the codeword yield a decoded value that is unrelated to the original message. Our results are as follows: -) For the case of bit-wise independent tampering, we establish the existence of rate-one continuously non-malleable codes with information-theoretic security, in the plain model. -) For the case of split-state tampering, we establish the existence of rate-one continuously non-malleable codes with computational security, in the (non-programmable) random oracle model. We further exhibit a rate-1/2 code and a rate-one code in the common reference string model, but the latter only withstands *non-adaptive* tampering. It is well known that computational security is inherent for achieving continuous non-malleability in the split-state model (even in the presence of non-adaptive tampering). Continuously non-malleable codes are useful for protecting *arbitrary* cryptographic primitives against related-key attacks, as well as for constructing non-malleable public-key encryption schemes. Our results directly improve the efficiency of these applications

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

Upper and Lower Bounds for Continuous Non-Malleable Codes

Recently, Faust et al. (TCC\u2714) introduced the notion of continuous non-malleable codes (CNMC), which provides stronger security guarantees than standard non-malleable codes, by allowing an adversary to tamper with the codeword in continuous way instead of one-time tampering. They also showed that CNMC with information theoretic security cannot be constructed in 2-split-state tampering model, and presented a construction of the same in CRS (common reference string) model using collision-resistant hash functions and non-interactive zero-knowledge proofs. In this work, we ask if it is possible to construct CNMC from weaker assumptions. We answer this question by presenting lower as well as upper bounds. Specifically, we show that it is impossible to construct 2-split-state CNMC, with no CRS, for one-bit messages from any falsifiable assumption, thus establishing the lower bound. We additionally provide an upper bound by constructing 2-split-state CNMC for one-bit messages, assuming only the existence of a family of injective one way functions. We also present a construction of 4-split-state CNMC for multi-bit messages in CRS model from the same assumptions. Additionally, we present definitions of the following new primitives: (1) One-to-one commitments, and (2) Continuous Non-Malleable Randomness Encoders, which may be of independent interest

Quantum secure non-malleable randomness encoder and its applications

"Non-Malleable Randomness Encoder"(NMRE) was introduced by Kanukurthi, Obbattu, and Sekar~[KOS18] as a useful cryptographic primitive helpful in the construction of non-malleable codes. To the best of our knowledge, their construction is not known to be quantum secure. We provide a construction of a first rate-$1/2$, $2$-split, quantum secure NMRE and use this in a black-box manner, to construct for the first time the following: 1) rate $1/11$, $3$-split, quantum non-malleable code, 2) rate $1/3$, $3$-split, quantum secure non-malleable code, 3) rate $1/5$, $2$-split, average case quantum secure non-malleable code.Comment: arXiv admin note: text overlap with arXiv:2308.0646

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