Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures

In an $\ell$ out of $n$ threshold scheme, $\ell$ out of $n$ members must cooperate to recover a secret. A kleptographic attack is a backdoor which can be implemented in an algorithm and further used to retrieve a user\u27s secret key. We combine the notions of threshold scheme and kleptographic attack to construct the first $\ell$ out of $n$ threshold kleptographic attack on discrete logarithm based digital signatures and prove its security in the standard and random oracle models

Communicating Through Subliminal-Free Signatures

By exploiting the inherent randomness used by certain digital signature protocols, subliminal channels can subvert these protocols without degrading their security. Due to their nature, these channels cannot be easily detected by an outside observer. Therefore, they pose a severe challenge for protocol designers. More precisely, designers consider certain assumptions implicitly, but in reality these assumptions turn out to be false or cannot be enforced or verified. In this paper we exemplify exactly such a situation by presenting several subliminal channels with a small capacity in Zhang et al. and Dong et al.\u27s subliminal-free signature protocols

Subliminal channels in post-quantum digital signature schemes

We analyze the digital signatures schemes submitted to NIST\u27s Post-Quantum Cryptography Standardization Project in search for subliminal channels

Kleptography and steganography in blockchains

Despite its vast proliferation, the blockchain technology is still evolving, and witnesses continuous technical innovations to address its numerous unresolved issues. An example of these issues is the excessive electrical power consumed by some consensus protocols. Besides, although various media reports have highlighted the existence of objectionable content in blockchains, this topic has not received sufficient research. Hence, this work investigates the threat and deterrence of arbitrary-content insertion in public blockchains, which poses a legal, moral, and technical challenge. In particular, the overall aim of this work is to thoroughly study the risk of manipulating the implementation of randomized cryptographic primitives in public blockchains to mount kleptographic attacks, establish steganographic communication, and store arbitrary content. As part of our study, we present three new kleptographic attacks on two of the most commonly used digital signatures: ring signature and ECDSA. We also demonstrate our kleptographic attacks on two real cryptocurrencies: Bytecoin and Monero. Moreover, we illustrate the plausibility of hijacking public blockchains to establish steganographic channels. Particularly, we design, implement, and evaluate the first blockchain-based broadcast communication tool on top of a real-world cryptocurrency. Furthermore, we explain the detrimental consequences of kleptography and steganography on the users and the future of the blockchain technology. Namely, we show that kleptography can be used to surreptitiously steal the users' secret signing keys, which are the most valuable and guarded secret in public blockchains. After losing their keys, users of cryptocurrencies will inevitably lose their funds. In addition, we clarify that steganography can be used to establish subliminal communication and secretly store arbitrary content in public blockchains, which turns them into cheap cyberlockers. Consequently, the participation in such blockchains, which are known to store unethical content, can be criminalized, hindering the future adoption of blockchains. After discussing the adverse effects of kleptographic and steganographic attacks on blockchains, we survey all of the existing techniques that can defend against these attacks. Finally, due to the shortcomings of the available techniques, we propose four countermeasures that ensure kleptography and steganography-resistant public blockchains. Our countermeasures include two new cryptographic primitives and a generic steganographyresistant blockchain framework (SRBF). This framework presents a universal solution that deters steganography and practically achieves the right to be forgotten (RtbF) in blockchains, which represents a regulatory challenge for current immutable blockchains

Zero-Knowledge Arguments for Matrix-Vector Relations and Lattice-Based Group Encryption

International audienceGroup encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ Z m×n q , s ∈ Z n q and a small-norm e ∈ Z m which underlie a public vector b = X · s + e ∈ Z m q while simultaneously proving that the matrix X ∈ Z m×n q has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting

On Foundations of Protecting Computations

Information technology systems have become indispensable to uphold our way of living, our economy and our safety. Failure of these systems can have devastating effects. Consequently, securing these systems against malicious intentions deserves our utmost attention. Cryptography provides the necessary foundations for that purpose. In particular, it provides a set of building blocks which allow to secure larger information systems. Furthermore, cryptography develops concepts and tech- niques towards realizing these building blocks. The protection of computations is one invaluable concept for cryptography which paves the way towards realizing a multitude of cryptographic tools. In this thesis, we contribute to this concept of protecting computations in several ways. Protecting computations of probabilistic programs. An indis- tinguishability obfuscator (IO) compiles (deterministic) code such that it becomes provably unintelligible. This can be viewed as the ultimate way to protect (deterministic) computations. Due to very recent research, such obfuscators enjoy plausible candidate constructions. In certain settings, however, it is necessary to protect probabilistic com- putations. The only known construction of an obfuscator for probabilistic programs is due to Canetti, Lin, Tessaro, and Vaikuntanathan, TCC, 2015 and requires an indistinguishability obfuscator which satisfies extreme security guarantees. We improve this construction and thereby reduce the require- ments on the security of the underlying indistinguishability obfuscator. (Agrikola, Couteau, and Hofheinz, PKC, 2020) Protecting computations in cryptographic groups. To facilitate the analysis of building blocks which are based on cryptographic groups, these groups are often overidealized such that computations in the group are protected from the outside. Using such overidealizations allows to prove building blocks secure which are sometimes beyond the reach of standard model techniques. However, these overidealizations are subject to certain impossibility results. Recently, Fuchsbauer, Kiltz, and Loss, CRYPTO, 2018 introduced the algebraic group model (AGM) as a relaxation which is closer to the standard model but in several aspects preserves the power of said overidealizations. However, their model still suffers from implausibilities. We develop a framework which allows to transport several security proofs from the AGM into the standard model, thereby evading the above implausi- bility results, and instantiate this framework using an indistinguishability obfuscator. (Agrikola, Hofheinz, and Kastner, EUROCRYPT, 2020) Protecting computations using compression. Perfect compression algorithms admit the property that the compressed distribution is truly random leaving no room for any further compression. This property is invaluable for several cryptographic applications such as “honey encryption” or password-authenticated key exchange. However, perfect compression algorithms only exist for a very small number of distributions. We relax the notion of compression and rigorously study the resulting notion which we call “pseudorandom encodings”. As a result, we identify various surprising connections between seemingly unrelated areas of cryptography. Particularly, we derive novel results for adaptively secure multi-party computation which allows for protecting computations in distributed settings. Furthermore, we instantiate the weakest version of pseudorandom encodings which suffices for adaptively secure multi-party computation using an indistinguishability obfuscator. (Agrikola, Couteau, Ishai, Jarecki, and Sahai, TCC, 2020

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents

Democracy Enhancing Technologies: Toward deployable and incoercible E2E elections

End-to-end verifiable election systems (E2E systems) provide a provably correct tally while maintaining the secrecy of each voter's ballot, even if the voter is complicit in demonstrating how they voted. Providing voter incoercibility is one of the main challenges of designing E2E systems, particularly in the case of internet voting. A second challenge is building deployable, human-voteable E2E systems that conform to election laws and conventions. This dissertation examines deployability, coercion-resistance, and their intersection in election systems. In the course of this study, we introduce three new election systems, (Scantegrity, Eperio, and Selections), report on two real-world elections using E2E systems (Punchscan and Scantegrity), and study incoercibility issues in one deployed system (Punchscan). In addition, we propose and study new practical primitives for random beacons, secret printing, and panic passwords. These are tools that can be used in an election to, respectively, generate publicly verifiable random numbers, distribute the printing of secrets between non-colluding printers, and to covertly signal duress during authentication. While developed to solve specific problems in deployable and incoercible E2E systems, these techniques may be of independent interest

Advances in cryptographic voting systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 241-254).Democracy depends on the proper administration of popular elections. Voters should receive assurance that their intent was correctly captured and that all eligible votes were correctly tallied. The election system as a whole should ensure that voter coercion is unlikely, even when voters are willing to be influenced. These conflicting requirements present a significant challenge: how can voters receive enough assurance to trust the election result, but not so much that they can prove to a potential coercer how they voted? This dissertation explores cryptographic techniques for implementing verifiable, secret-ballot elections. We present the power of cryptographic voting, in particular its ability to successfully achieve both verifiability and ballot secrecy, a combination that cannot be achieved by other means. We review a large portion of the literature on cryptographic voting. We propose three novel technical ideas: 1. a simple and inexpensive paper-base cryptographic voting system with some interesting advantages over existing techniques, 2. a theoretical model of incoercibility for human voters with their inherent limited computational ability, and a new ballot casting system that fits the new definition, and 3. a new theoretical construct for shuffling encrypted votes in full view of public observers.by Ben Adida.Ph.D