Tight Upper and Lower Bounds for Leakage-Resilient, Locally Decodable and Updatable Non-Malleable Codes

In a recent result, Dachman-Soled et al.~(TCC \u2715) proposed a new notion called locally decodable and updatable non-malleable codes, which informally, provides the security guarantees of a non-malleable code while also allowing for efficient random access. They also considered locally decodable and updatable non-malleable codes that are leakage-resilient, allowing for adversaries who continually leak information in addition to tampering. Unfortunately, the locality of their construction in the continual setting was Omega(log n), meaning that if the original message size was n, then Omega(log n) positions of the codeword had to be accessed upon each decode and update instruction. In this work, we ask whether super-constant locality is inherent in this setting. We answer the question affirmatively by showing tight upper and lower bounds. Specifically, in any threat model which allows for a rewind attack-wherein the attacker leaks a small amount of data, waits for the data to be overwritten and then writes the original data back-we show that a locally decodable and updatable non-malleable code with block size Chi in poly(lambda) number of bits requires locality delta(n) in omega(1), where n = poly(lambda) is message length and lambda is security parameter. On the other hand, we re-visit the threat model of Dachman-Soled et al.~(TCC \u2715)-which indeed allows the adversary to launch a rewind attack-and present a construction of a locally decodable and updatable non-malleable code with block size Chi in Omega(lambda^{1/mu}) number of bits (for constant 0 < mu < 1) with locality delta(n), for any delta(n) in omega(1), and n = poly(lambda)

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

Extending The Applicability of Non-Malleable Codes

Modern cryptographic systems provide provable security guarantees as long as secret keys of the system remain confidential. However, if adversary learns some bits of information about the secret keys the security of the system can be breached. Side-channel attacks (like power analysis, timing analysis etc.) are one of the most effective tools employed by the adversaries to learn information pertaining to cryptographic secret keys. An adversary can also tamper with secret keys (say flip some bits) and observe the modified behavior of the cryptosystem, thereby leaking information about the secret keys. Dziembowski et al. (JACM 2018) defined the notion of non-malleable codes, a tool to protect memory against tampering. Non-malleable codes ensure that, when a codeword (generated by encoding an underlying message) is modified by some tampering function in a given tampering class, if the decoding of tampered codeword is incorrect then the decoded message is independent of the original message. In this dissertation, we focus on improving different aspects of non-malleable codes. Specifically, (1) we extend the class of tampering functions and present explicit constructions as well as general frameworks for constructing non-malleable codes. While most prior work considered ``compartmentalized" tampering functions, which modify parts of the codeword independently, we consider classes of tampering functions which can tamper with the entire codeword but are restricted in computational complexity. The tampering classes studied in this work include complexity classes $\mathsf{NC}^0$, and $\mathsf{AC}^0$. Also, earlier works focused on constructing non-malleable codes from scratch for different tampering classes, in this work we present a general framework for constructing non-malleable codes based on average-case hard problems for specific tampering families, and we instantiate our framework for various tampering classes including $\mathsf{AC}^0$. (2) The locality of code is the number of codeword blocks required to be accessed in order to decode/update a single block in the underlying message. We improve efficiency and usability by studying the optimal locality of non-malleable codes. We show that locally decodable and updatable non-malleable codes cannot have constant locality. We also give a matching upper bound that improves the locality of previous constructions. (3) We investigate a stronger variant of non-malleable codes called continuous non-malleable codes, which are known to be impossible to construct without computational assumptions. We show that setup assumptions such as common reference string (CRS) are also necessary to construct this stronger primitive. We present construction of continuous non-malleable codes in CRS model from weaker computational assumptions than assumptions used in prior work

(Continuous) Non-malleable Codes for Partial Functions with Manipulation Detection and Light Updates

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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

Non-Malleable Codes for Partial Functions with Manipulation Detection

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs (ICS \u2710) and its main application is the protection of cryptographic devices against tampering attacks on memory. In this work, we initiate a comprehensive study on non-malleable codes for the class of partial functions, that read/write on an arbitrary subset of codeword bits with specific cardinality. Our constructions are efficient in terms of information rate, while allowing the attacker to access asymptotically almost the entire codeword. In addition, they satisfy a notion which is stronger than non-malleability, that we call non-malleability with manipulation detection, guaranteeing that any modified codeword decodes to either the original message or to $\bot$. Finally, our primitive implies All-Or-Nothing Transforms (AONTs) and as a result our constructions yield efficient AONTs under standard assumptions (only one-way functions), which, to the best of our knowledge, was an open question until now. In addition to this, we present a number of additional applications of our primitive in tamper resilience

Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting

Interactive Non-Malleable Codes were introduced by Fleischhacker et al. (TCC 2019) in the two party setting with synchronous tampering. The idea of this type of non-malleable code is that it "encodes" an interactive protocol in such a way that, even if the messages are tampered with according to some class F of tampering functions, the result of the execution will either be correct, or completely unrelated to the inputs of the participating parties. In the synchronous setting the adversary is able to modify the messages being exchanged but cannot drop messages nor desynchronize the two parties by first running the protocol with the first party and then with the second party. In this work, we define interactive non-malleable codes in the non-synchronous multi-party setting and construct such interactive non-malleable codes for the class F^s_bounded of bounded-state tampering functions

Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting

Interactive Non-Malleable Codes were introduced by Fleischhacker et al. (TCC 2019) in the two party setting with synchronous tampering. The idea of this type of non-malleable code is that it encodes an interactive protocol in such a way that, even if the messages are tampered with according to some class $\mathcal{F}$ of tampering functions, the result of the execution will either be correct, or completely unrelated to the inputs of the participating parties. In the synchronous setting the adversary is able to modify the messages being exchanged but cannot drop messages nor desynchronize the two parties by first running the protocol with the first party and then with the second party. In this work, we define interactive non-malleable codes in the non-synchronous multi-party setting and construct such interactive non-malleable codes for the class $\mathcal{F}^{s}_{\textsf{bounded}}$ of bounded-state tampering functions. The construction is applicable to any multi-party protocol with a fixed message topology

Survey: Non-malleable code in the split-state model

Non-malleable codes are a natural relaxation of error correction and error detection codes applicable in scenarios where error-correction or error-detection is impossible. Over the last decade, non-malleable codes have been studied for a wide variety of tampering families. Among the most well studied of these is the split-state family of tampering channels, where the codeword is split into two or more parts and each part is tampered independently. We survey various constructions and applications of non-malleable codes in the split-state model