Delegating Quantum Computation in the Quantum Random Oracle Model

A delegation scheme allows a computationally weak client to use a server's resources to help it evaluate a complex circuit without leaking any information about the input (other than its length) to the server. In this paper, we consider delegation schemes for quantum circuits, where we try to minimize the quantum operations needed by the client. We construct a new scheme for delegating a large circuit family, which we call "C+P circuits". "C+P" circuits are the circuits composed of Toffoli gates and diagonal gates. Our scheme is non-interactive, requires very little quantum computation from the client (proportional to input length but independent of the circuit size), and can be proved secure in the quantum random oracle model, without relying on additional assumptions, such as the existence of fully homomorphic encryption. In practice the random oracle can be replaced by an appropriate hash function or block cipher, for example, SHA-3, AES. This protocol allows a client to delegate the most expensive part of some quantum algorithms, for example, Shor's algorithm. The previous protocols that are powerful enough to delegate Shor's algorithm require either many rounds of interactions or the existence of FHE. The protocol requires asymptotically fewer quantum gates on the client side compared to running Shor's algorithm locally. To hide the inputs, our scheme uses an encoding that maps one input qubit to multiple qubits. We then provide a novel generalization of classical garbled circuits ("reversible garbled circuits") to allow the computation of Toffoli circuits on this encoding. We also give a technique that can support the computation of phase gates on this encoding. To prove the security of this protocol, we study key dependent message(KDM) security in the quantum random oracle model. KDM security was not previously studied in quantum settings.Comment: 41 pages, 1 figures. Update to be consistent with the proceeding versio

Seeking Anonymity in an Internet Panopticon

Obtaining and maintaining anonymity on the Internet is challenging. The state of the art in deployed tools, such as Tor, uses onion routing (OR) to relay encrypted connections on a detour passing through randomly chosen relays scattered around the Internet. Unfortunately, OR is known to be vulnerable at least in principle to several classes of attacks for which no solution is known or believed to be forthcoming soon. Current approaches to anonymity also appear unable to offer accurate, principled measurement of the level or quality of anonymity a user might obtain. Toward this end, we offer a high-level view of the Dissent project, the first systematic effort to build a practical anonymity system based purely on foundations that offer measurable and formally provable anonymity properties. Dissent builds on two key pre-existing primitives - verifiable shuffles and dining cryptographers - but for the first time shows how to scale such techniques to offer measurable anonymity guarantees to thousands of participants. Further, Dissent represents the first anonymity system designed from the ground up to incorporate some systematic countermeasure for each of the major classes of known vulnerabilities in existing approaches, including global traffic analysis, active attacks, and intersection attacks. Finally, because no anonymity protocol alone can address risks such as software exploits or accidental self-identification, we introduce WiNon, an experimental operating system architecture to harden the uses of anonymity tools such as Tor and Dissent against such attacks.Comment: 8 pages, 10 figure

Lattice-Based proof of a shuffle

In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft

Shorter lattice-based zero-knowledge proofs for the correctness of a shuffle

In an electronic voting procedure, mixing networks are used to ensure anonymity of the casted votes. Each node of the network re-encrypts the input list of ciphertexts and randomly permutes it in a process named shuffle, and must prove (in zero-knowledge) that the process was applied honestly. To maintain security of such a process in a post-quantum scenario, new proofs are based on different mathematical assumptions, such as lattice-based problems. Nonetheless, the best lattice-based protocols to ensure verifiable shuffling have linear communication complexity on N, the number of shuffled ciphertexts. In this paper we propose the first sub-linear (on N) post-quantum zero-knowledge argument for the correctness of a shuffle, for which we have mainly used two ideas: arithmetic circuit satisfiability results from Baum et al. (CRYPTO'2018) and Beneš networks to model a permutation of N elements. The achieved communication complexity of our protocol with respect to N is O(v(N)log^2(N)), but we will also highlight its dependency on other important parameters of the underlying lattice ingredients.The work is partially supported by the Spanish Ministerio de Ciencia e Innovaci´on (MICINN), under Project PID2019-109379RB-I00 and by the European Union PROMETHEUS project (Horizon 2020 Research and Innovation Program, grant 780701). Authors thank Tjerand Silde for pointing out an incorrect set of parameters (Section 4.1) that we had proposed in a previous version of the manuscript.Postprint (author's final draft

Verifiable Elections That Scale for Free

In order to guarantee a fair and transparent voting process, electronic voting schemes must be verifiable. Most of the time, however, it is important that elections also be anonymous. The notion of a verifiable shuffle describes how to satisfy both properties at the same time: ballots are submitted to a public bulletin board in encrypted form, verifiably shuffled by several mix servers (thus guaranteeing anonymity), and then verifiably decrypted by an appropriate threshold decryption mechanism. To guarantee transparency, the intermediate shuffles and decryption results, together with proofs of their correctness, are posted on the bulletin board throughout this process. In this paper, we present a verifiable shuffle and threshold decryption scheme in which, for security parameter k, L voters, M mix servers, and N decryption servers, the proof that the end tally corresponds to the original encrypted ballots is only O(k(L + M + N)) bits long. Previous verifiable shuffle constructions had proofs of size O(kLM + kLN), which, for elections with thousands of voters, mix servers, and decryption servers, meant that verifying an election on an ordinary computer in a reasonable amount of time was out of the question. The linchpin of each construction is a controlled-malleable proof (cm-NIZK), which allows each server, in turn, to take a current set of ciphertexts and a proof that the computation done by other servers has proceeded correctly so far. After shuffling or partially decrypting these ciphertexts, the server can also update the proof of correctness, obtaining as a result a cumulative proof that the computation is correct so far. In order to verify the end result, it is therefore sufficient to verify just the proof produced by the last server