The Crypto-democracy and the Trustworthy

In the current architecture of the Internet, there is a strong asymmetry in terms of power between the entities that gather and process personal data (e.g., major Internet companies, telecom operators, cloud providers, ...) and the individuals from which this personal data is issued. In particular, individuals have no choice but to blindly trust that these entities will respect their privacy and protect their personal data. In this position paper, we address this issue by proposing an utopian crypto-democracy model based on existing scientific achievements from the field of cryptography. More precisely, our main objective is to show that cryptographic primitives, including in particular secure multiparty computation, offer a practical solution to protect privacy while minimizing the trust assumptions. In the crypto-democracy envisioned, individuals do not have to trust a single physical entity with their personal data but rather their data is distributed among several institutions. Together these institutions form a virtual entity called the Trustworthy that is responsible for the storage of this data but which can also compute on it (provided first that all the institutions agree on this). Finally, we also propose a realistic proof-of-concept of the Trustworthy, in which the roles of institutions are played by universities. This proof-of-concept would have an important impact in demonstrating the possibilities offered by the crypto-democracy paradigm.Comment: DPM 201

Practical and Foundational Aspects of Secure Computation

Il y a des problemes qui semblent impossible a resoudre sans l'utilisation d'un tiers parti honnete. Comment est-ce que deux millionnaires peuvent savoir qui est le plus riche sans dire a l'autre la valeur de ses biens ? Que peut-on faire pour prevenir les collisions de satellites quand les trajectoires sont secretes ? Comment est-ce que les chercheurs peuvent apprendre les liens entre des medicaments et des maladies sans compromettre les droits prives du patient ? Comment est-ce qu'une organisation peut ecmpecher le gouvernement d'abuser de l'information dont il dispose en sachant que l'organisation doit n'avoir aucun acces a cette information ? Le Calcul multiparti, une branche de la cryptographie, etudie comment creer des protocoles pour realiser de telles taches sans l'utilisation d'un tiers parti honnete. Les protocoles doivent etre prives, corrects, efficaces et robustes. Un protocole est prive si un adversaire n'apprend rien de plus que ce que lui donnerait un tiers parti honnete. Un protocole est correct si un joueur honnete recoit ce que lui donnerait un tiers parti honnete. Un protocole devrait bien sur etre efficace. Etre robuste correspond au fait qu'un protocole marche meme si un petit ensemble des joueurs triche. On demontre que sous l'hypothese d'un canal de diusion simultane on peut echanger la robustesse pour la validite et le fait d'etre prive contre certains ensembles d'adversaires. Le calcul multiparti a quatre outils de base : le transfert inconscient, la mise en gage, le partage de secret et le brouillage de circuit. Les protocoles du calcul multiparti peuvent etre construits avec uniquements ces outils. On peut aussi construire les protocoles a partir d'hypoth eses calculatoires. Les protocoles construits a partir de ces outils sont souples et peuvent resister aux changements technologiques et a des ameliorations algorithmiques. Nous nous demandons si l'efficacite necessite des hypotheses de calcul. Nous demontrons que ce n'est pas le cas en construisant des protocoles efficaces a partir de ces outils de base. Cette these est constitue de quatre articles rediges en collaboration avec d'autres chercheurs. Ceci constitue la partie mature de ma recherche et sont mes contributions principales au cours de cette periode de temps. Dans le premier ouvrage presente dans cette these, nous etudions la capacite de mise en gage des canaux bruites. Nous demontrons tout d'abord une limite inferieure stricte qui implique que contrairement au transfert inconscient, il n'existe aucun protocole de taux constant pour les mises en gage de bit. Nous demontrons ensuite que, en limitant la facon dont les engagements peuvent etre ouverts, nous pouvons faire mieux et meme un taux constant dans certains cas. Ceci est fait en exploitant la notion de cover-free families . Dans le second article, nous demontrons que pour certains problemes, il existe un echange entre robustesse, la validite et le prive. Il s'effectue en utilisant le partage de secret veriable, une preuve a divulgation nulle, le concept de fantomes et une technique que nous appelons les balles et les bacs. Dans notre troisieme contribution, nous demontrons qu'un grand nombre de protocoles dans la litterature basee sur des hypotheses de calcul peuvent etre instancies a partir d'une primitive appelee Transfert Inconscient Veriable, via le concept de Transfert Inconscient Generalise. Le protocole utilise le partage de secret comme outils de base. Dans la derniere publication, nous counstruisons un protocole efficace avec un nombre constant de rondes pour le calcul a deux parties. L'efficacite du protocole derive du fait qu'on remplace le coeur d'un protocole standard par une primitive qui fonctionne plus ou moins bien mais qui est tres peu couteux. On protege le protocole contre les defauts en utilisant le concept de privacy amplication .There are seemingly impossible problems to solve without a trusted third-party. How can two millionaires learn who is the richest when neither is willing to tell the other how rich he is? How can satellite collisions be prevented when the trajectories are secret? How can researchers establish correlations between diseases and medication while respecting patient confidentiality? How can an organization insure that the government does not abuse the knowledge that it possesses even though such an organization would be unable to control that information? Secure computation, a branch of cryptography, is a eld that studies how to generate protocols for realizing such tasks without the use of a trusted third party. There are certain goals that such protocols should achieve. The rst concern is privacy: players should learn no more information than what a trusted third party would give them. The second main goal is correctness: players should only receive what a trusted third party would give them. The protocols should also be efficient. Another important property is robustness, the protocols should not abort even if a small set of players is cheating. Secure computation has four basic building blocks : Oblivious Transfer, secret sharing, commitment schemes, and garbled circuits. Protocols can be built based only on these building blocks or alternatively, they can be constructed from specific computational assumptions. Protocols constructed solely from these primitives are flexible and are not as vulnerable to technological or algorithmic improvements. Many protocols are nevertheless based on computational assumptions. It is important to ask if efficiency requires computational assumptions. We show that this is not the case by building efficient protocols from these primitives. It is the conclusion of this thesis that building protocols from black-box primitives can also lead to e cient protocols. This thesis is a collection of four articles written in collaboration with other researchers. This constitutes the mature part of my investigation and is my main contributions to the field during that period of time. In the first work presented in this thesis we study the commitment capacity of noisy channels. We first show a tight lower bound that implies that in contrast to Oblivious Transfer, there exists no constant rate protocol for bit commitments. We then demonstrate that by restricting the way the commitments can be opened, we can achieve better efficiency and in particular cases, a constant rate. This is done by exploiting the notion of cover-free families. In the second article, we show that for certain problems, there exists a trade-off between robustness, correctness and privacy. This is done by using verifiable secret sharing, zero-knowledge, the concept of ghosts and a technique which we call \balls and bins". In our third contribution, we show that many protocols in the literature based on specific computational assumptions can be instantiated from a primitive known as Verifiable Oblivious Transfer, via the concept of Generalized Oblivious Transfer. The protocol uses secret sharing as its foundation. In the last included publication, we construct a constant-round protocol for secure two-party computation that is very efficient and only uses black-box primitives. The remarkable efficiency of the protocol is achieved by replacing the core of a standard protocol by a faulty but very efficient primitive. The fault is then dealt with by a non-trivial use of privacy amplification

Constant-round secure two-party computation from a linear number of oblivious transfer

We construct a protocol for constant round Two-Party Secure Function Evaluation in the standard model which improves previous protocols in several ways. We are able to reduce the number of calls to Oblivious Transfer by a factor proportional to the security parameter. In addition to being more efficient than previous instantiations, our protocol only requires black box calls to OT and Commitment. This is achieved by the use of a faulty variant of the Cut-and-Choose OT. The concepts of Garbling Schemes, faulty Cut-and-Choose Oblivious Transfer and Privacy Amplification are combined using the Cut-and-Choose paradigm to obtain the final protocol

Authenticated Garbling and Efficient Maliciously Secure Two-Party Computation

We propose a simple and efficient framework for obtaining efficient constant-round protocols for maliciously secure two-party computation. Our framework uses a function-independent preprocessing phase to generate authenticated information for the two parties; this information is then used to construct a single ``authenticated\u27\u27 garbled circuit which is transmitted and evaluated. We also show how to efficiently instantiate the preprocessing phase by designing a highly optimized version of the TinyOT protocol by Nielsen et al. Our overall protocol outperforms existing work in both the single-execution and amortized settings, with or without preprocessing: - In the single-execution setting, our protocol evaluates an AES circuit with malicious security in 37 ms with an online time of just 1 ms. Previous work with the best online time (also 1 ms) requires 124 ms in total; previous work with the best total time requires 62 ms (with 14 ms online time). - If we amortize the computation over 1024 executions, each AES computation requires just 6.7 ms with roughly the same online time as above. The best previous work in the amortized setting has roughly the same total time but does not support function-independent preprocessing. Our work shows that the performance penalty for maliciously secure two-party computation (as compared to semi-honest security) is much smaller than previously believed

Security of Linear Secret-Sharing Schemes against Mass Surveillance

Following the line of work presented recently by Bellare, Paterson and Rogaway, we formalize and investigate the resistance of linear secret-sharing schemes to mass surveillance. This primitive is widely used to design IT systems in the modern computer world, and often it is implemented by a proprietary code that the provider (“big brother”) could manipulate to covertly violate the privacy of the users (by implementing Algorithm-Substitution Attacks or ASAs). First, we formalize the security notion that expresses the goal of big brother and prove that for any linear secret-sharing scheme there exists an undetectable subversion of it that efficiently allows surveillance. Second, we formalize the security notion that assures that a sharing scheme is secure against ASAs and construct the first sharing scheme that meets this notion. This work could serve as an important building block towards constructing systems secure against mass surveillance

Secure Computation with Low Communication from Cross-checking

We construct new four-party protocols for secure computation that are secure against a single malicious corruption. Our protocols can perform computations over a binary ring, and require sending just 1.5 ring elements per party, per gate. In the special case of Boolean circuits, this amounts to sending 1.5 bits per party, per gate. One of our protocols is robust, yet requires almost no additional communication. Our key technique can be viewed as a variant of the “dual execution” approach, but, because we rely on four parties instead of two, we can avoid any leakage, achieving the standard notion of security

Efficient Generic Zero-Knowledge Proofs from Commitments

Even though Zero-knowledge has existed for more than 30 years, few generic constructions for Zero-knowledge exist. In this paper we present a new kind of commitment scheme on which we build a novel and efficient Zero-knowledge protocol for circuit satisfiability. We can prove knowledge of the AES-key which map a particular plaintext to a particular ciphertext in less than 4 seconds with a soundness error of $2^{-40}$. Our protocol only requires a number of commitments proportional to the security parameter with a small constant (roughly 5)

Highly Efficient OT-Based Multiplication Protocols

We present a new OT-based two-party multiplication protocol that is almost as efficient as Gilboa\u27s semi-honest protocol (Crypto \u2799), but has a high-level of security against malicious adversaries without further compilation. The achieved security suffices for many applications, and, assuming DDH, can be cheaply compiled into full security

Server-Aided Two-Party Computation with Minimal Connectivity in the Simultaneous Corruption Model

We consider secure two-party computation in the client-server model. In our scenario, two adversaries operate \emph{separately but simultaneously}, each of them corrupting one of the parties and a restricted subset of servers that they interact with. We model security in this setting via the local universal composability framework introduced by Canetti and Vald and show that information-theoretically secure two-party computation is possible if and only if there is always at least one server which remains uncorrupted. Moreover, in our protocols each of the servers only needs to communicate with the two clients, i.e. no messages are exchanged directly between servers. This communication pattern is minimal

Fast Secure Multiparty ECDSA with Practical Distributed Key Generation and Applications to Cryptocurrency Custody

ECDSA is a standardized signing algorithm that is widely used in TLS, code signing, cryptocurrency and more. Due to its importance, the problem of securely computing ECDSA in a distributed manner (known as threshold signing) has received considerable interest. Despite this interest, however, as of the time of publication of the conference version of this paper ([Lindel and Nof, ACM SIGSAC 18\u27), there had been no full threshold solution for more than two parties (meaning that any t-out-of-n parties can sign, security is preserved for any t−1 or fewer corrupted parties, and t ≤ n can be any value) that supports practical key distribution. All previous solutions for this functionality utilized Paillier homomorphic encryption, and efficient distributed Paillier key generation for more than two parties is not known. In this paper, we present the first (again, for the conference version publication time) truly practical full threshold ECDSA signing protocol that has fast signing and key generation. This solves an old open problem and opens the door to many practical uses of threshold ECDSA signing that are in demand today. One of these applications is the construction of secure cryptocurrency wallets (where key-shares are spread over multiple devices, and so are hard to steal) and cryptocurrency custody solutions (where large sums of invested cryptocurrency are strongly protected by splitting the key between a bank/financial institution, the customer who owns the currency, and possibly a third-party trustee, in multiple shares at each). There is growing practical interest in such solutions, but prior to our work, these could not be deployed due to the need for a distributed key generation