Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack

Open Voting Client Architecture and Op-Ed Voting: A Novel Framework for Solving Requirement Conflicts in Secret Ballot Elections

Building voting systems for secret ballot elections has many challenges and is the subject of significant academic research efforts. These challenges come from conflicting requirements. In this paper, we introduce a novel architectural approach to voting system construction that may help satisfy conflicting requirements and increase voter satisfaction. Our design, called Open Voting Client Architecture, defines a voting system architectural approach that can harness the power of individualized voting clients. In this work, we contribute a voting system reference architecture to depict the current voting system construction and then use it to define Open Voting Client Architecture. We then detail a specific implementation called Op-Ed Voting to evaluate the security of Open Voting Client Architecture systems. We show that Op-Ed Voting, using voters\u27 personal devices in an end-to-end verifiable protocol, can potentially improve usability and accessibility for voters while also satisfying security requirements for electronic voting

A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

A smart contract system for decentralized borda count voting

In this article, we propose the first self-tallying decentralized e-voting protocol for a ranked-choice voting system based on Borda count. Our protocol does not need any trusted setup or tallying authority to compute the tally. The voters interact through a publicly accessible bulletin board for executing the protocol in a way that is publicly verifiable. Our main protocol consists of two rounds. In the first round, the voters publish their public keys, and in the second round they publish their randomized ballots. All voters provide Non-interactive Zero-Knowledge (NIZK) proofs to show that they have been following the protocol specification honestly without revealing their secret votes. At the end of the election, anyone including a third-party observer will be able to compute the tally without needing any tallying authority. We provide security proofs to show that our protocol guarantees the maximum privacy for each voter. We have implemented our protocol using Ethereum's blockchain as a public bulletin board to record voting operations as publicly verifiable transactions. The experimental data obtained from our tests show the protocol's potential for the real-world deployment

Cryptographic reverse firewalls for interactive proof systems

We study interactive proof systems (IPSes) in a strong adversarial setting where the machines of *honest parties* might be corrupted and under control of the adversary. Our aim is to answer the following, seemingly paradoxical, questions: - Can Peggy convince Vic of the veracity of an NP statement, without leaking any information about the witness even in case Vic is malicious and Peggy does not trust her computer? - Can we avoid that Peggy fools Vic into accepting false statements, even if Peggy is malicious and Vic does not trust her computer? At EUROCRYPT 2015, Mironov and Stephens-Davidowitz introduced cryptographic reverse firewalls (RFs) as an attractive approach to tackling such questions. Intuitively, a RF for Peggy/Vic is an external party that sits between Peggy/Vic and the outside world and whose scope is to sanitize Peggy's/Vic's incoming and outgoing messages in the face of subversion of her/his computer, e.g. in order to destroy subliminal channels. In this paper, we put forward several natural security properties for RFs in the concrete setting of IPSes. As our main contribution, we construct efficient RFs for different IPSes derived from a large class of Sigma protocols that we call malleable. A nice feature of our design is that it is completely transparent, in the sense that our RFs can be directly applied to already deployed IPSes, without the need to re-implement them

Vector commitments over rings and compressed Σ-protocols

Compressed Σ-Protocol Theory (CRYPTO 2020) presents an “alternative” to Bulletproofs that achieves the same communication complexity while adhering more elegantly to existing Σ -protocol theory, which enables their techniques to be directly applicable to other widely used settings in the context of “plug & play” algorithmics. Unfortunately, their techniques are restricted to arithmetic circuits over prime fields, which rules out the possibility of using more machine-friendly moduli such as powers of 2, which have proven to improve efficiency in applications. In this work we show that such techniques can be generalized to the case of arithmetic circuits modulo any number. This enables the use of powers of 2, which can prove to be beneficial for efficiency, but it also facilitates the use of other moduli that might prove useful in different applications. In order to achieve this, we first present an instantiation of the main building block of the theory of compressed Σ -protocols, namely compact vector commitments. Our construction, which may be of independent interest, is homomorphic modulo any positive integer m, a result that was not known in the literature before. Second, we generalize Compressed Σ-Protocol Theory from finite fields to Zm. The main challenge here is ensuring that there are large enough challenge sets as to fulfill the necessary soundness requirements, which is achieved by considering certain ring extensions. Our techniques have direct application for example to verifiable computation on homomorphically encrypted data

Implementation of a Secure Multiparty Computation Protocol

Secure multiparty computation (SMC) allows a set of parties to jointly compute a function on private inputs such that, they learn only the output of the function, and the correctness of the output is guaranteed even when a subset of the parties is controlled by an adversary. SMC allows data to be kept in an uncompromisable form and still be useful, and it also gives new meaning to data ownership, allowing data to be shared in a useful way while retaining its privacy. Thus, applications of SMC hold promise for addressing some of the security issues information-driven societies struggle with. In this thesis, we implement two SMC protocols. Our primary objective is to gain a solid understanding of the basic concepts related to SMC. We present a brief survey of the field, with focus on SMC based on secret sharing. In addition to the protocol im- plementations, we implement circuit randomization, a common technique for efficiency improvement. The implemented protocols are run on a simulator to securely evaluate some simple arithmetic functions, and the round complexities of the implemented protocols are compared. Finally, we attempt to extend the implementation to support more general computations

Practically Efficient Secure Computation of Rank-based Statistics Over Distributed Datasets

In this paper, we propose a practically efficient model for securely computing rank-based statistics, e.g., median, percentiles and quartiles, over distributed datasets in the malicious setting without leaking individual data privacy. Based on the binary search technique of Aggarwal et al. (EUROCRYPT \textquotesingle 04), we respectively present an interactive protocol and a non-interactive protocol, involving at most $\log ||R||$ rounds, where $||R||$ is the range size of the dataset elements. Besides, we introduce a series of optimisation techniques to reduce the round complexity. Our computing model is modular and can be instantiated with either homomorphic encryption or secret-sharing schemes. Compared to the state-of-the-art solutions, it provides stronger security and privacy while maintaining high efficiency and accuracy. Unlike differential-privacy-based solutions, it does not suffer a trade-off between accuracy and privacy. On the other hand, it only involves $O(N \log ||R||)$ time complexity, which is far more efficient than those bitwise-comparison-based solutions with $O(N^2\log ||R||)$ time complexity, where $N$ is the dataset size. Finally, we provide a UC-secure instantiation with the threshold Paillier cryptosystem and $\Sigma$-protocol zero-knowledge proofs of knowledge

Hash function requirements for Schnorr signatures

We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group representations such as those which occur in elliptic curve groups. We also show, via an argument in the generic group model, that these conditions are sufficient. Our hash function security requirements are variants of the standard notions of preimage and second preimage resistance. One of them is in fact equivalent to the Nostradamus attack by Kelsey and Kohno (Eurocrypt, Lecture Notes in Computer Science 4004: 183-200, 2006), and, when considering keyed compression functions, both are closely related to the ePre and eSec notions by Rogaway and Shrimpton (FSE, Lecture Notes in Computer Science 3017: 371-388, 2004). Our results have a number of interesting implications in practice. First, since security does not rely on the hash function being collision resistant, Schnorr signatures can still be securely instantiated with SHA-1/SHA-256, unlike DSA signatures. Second, we conjecture that our properties require O(2 n ) work to solve for a hash function with n-bit output, thereby allowing the use of shorter hashes and saving twenty-five percent in signature size. And third, our analysis does not reveal any significant difference in hardness between forging signatures and computing discrete logarithms, which plays down the importance of the loose reductions in existing random-oracle proofs, and seems to support the use of "normal-size” group