Securing Abe’s Mix-Net Against Malicious Verifiers via Witness Indistinguishability

Boyle, Elette; Klein, Saleet; Rosen, Alon; Segev, Gil

doi:10.1007/978-3-319-98113-0_15

Cited by 7 publications

(8 citation statements)

References 24 publications

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“…Indeed, a cyclic group G of prime order p has a vector space structure over the field Z p , and a group homomorphism f : G → G between groups of order p is also a Z p -vector homomorphism. 4 Let G be a generator of G. Given X ∈ G, a discrete logarithm DL proof of knowledge DL(w; G, X) asserts knowledge of w ∈ Z p with X = w • G (we denote this as w = DL G (X)). In the language above this is provided by…”

Section: Sigma-protocolsmentioning

confidence: 99%

YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model

Cascudo¹,

David²,

Garms³

et al. 2022

Lecture Notes in Computer Science

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Achieving adaptive (or proactive) security in cryptographic protocols is notoriously difficult due to the adversary's power to dynamically corrupt parties as the execution progresses. Inspired by the work of Benhamouda et al. in TCC 2020, Gentry et al. in CRYPTO 2021 introduced the YOSO (You Only Speak Once) model for constructing adaptively (or proactively) secure protocols in massively distributed settings (e.g. blockchains). In this model, instead of having all parties execute an entire protocol, smaller anonymous committees are randomly chosen to execute each individual round of the protocol. After playing their role, parties encrypt protocol messages towards the the next anonymous committee and erase their internal state before publishing their ciphertexts. However, a big challenge remains in realizing YOSO protocols: efficiently encrypting messages towards anonymous parties selected at random without learning their identities, while proving the encrypted messages are valid with respect to the protocol. In particular, the protocols of Benhamouda et al. and of Gentry et al. require showing ciphertexts contain valid shares of secret states. We propose concretely efficient methods for encrypting a protocol's secret state towards a random anonymous committee. We start by proposing a very simple and efficient scheme for encrypting messages towards randomly and anonymously selected parties. We then show constructions of publicly verifiable secret (re-)sharing (PVSS) schemes with concretely efficient proofs of (re-)share validity that can be generically instantiated from encryption schemes with certain linear homomorphic properties. In addition, we introduce a new PVSS with proof of sharing consisting of just two field elements, which as far as we know is the first achieving this, and may be of independent interest. Finally, we show that our PVSS schemes can be efficiently realized from our encyption scheme. * Ignacio Cascudo was supported by the Spanish Government under the project SecuRing (ref. PID2019-110873RJ-I00/AEI/10.13039/501100011033), by the Madrid Government as part of the program S2018/TCS-4339 (BLOQUES-CM) co-funded by EIE Funds of the European Union, and by a research grant from Nomadic Labs and the Tezos Foundation.† Bernardo David was supported by the Concordium Foundation and by the Independent Research Fund Denmark (IRFD) grants number 9040-00399B (TrA 2 C), 9131-00075B (PUMA) and 0165-00079B.‡ Lydia Garms was supported by a research grant from Nomadic Labs and the Tezos Foundation.§ Anders Konring was supported by the IRFD grant number 9040-00399B (TrA 2 C).

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Section: Sigma-protocolsmentioning

confidence: 99%

YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model

Cascudo¹,

David²,

Garms³

et al. 2022

Lecture Notes in Computer Science

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“…Our usage of the butterfly network draws inspiration from switching networks [1,10]. A novelty of our construction is the use of buckets so that multiple transactions can be present at the same position in an intermediate layer.…”

Section: Definition 21 (K-ary N-size Butterfly Network)mentioning

confidence: 99%

(∈, δ)-Indistinguishable Mixing for Cryptocurrencies

Liang

Karantaidou

Baldimtsi

et al. 2021

Proceedings on Privacy Enhancing Technologies

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We propose a new theoretical approach for building anonymous mixing mechanisms for cryptocurrencies. Rather than requiring a fully uniform permutation during mixing, we relax the requirement, insisting only that neighboring permutations are similarly likely. This is defined formally by borrowing from the definition of differential privacy. This relaxed privacy definition allows us to greatly reduce the amount of interaction and computation in the mixing protocol. Our construction achieves O(n·polylog(n)) computation time for mixing n addresses, whereas all other mixing schemes require O(n 2) total computation across all parties. Additionally, we support a smooth tolerance of fail-stop adversaries and do not require any trusted setup. We analyze the security of our generic protocol under the UC framework, and under a stand-alone, game-based definition. We finally describe an instantiation using ring signatures and confidential transactions.

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“…Note that we separate the shuffling in two well-differentiated parts / circuits, one for the re-encryption and one for the permutation. An alternative solution (used for instance in [12]) would be to add a re-randomization step in each switch gate of the Beneš network. However, the size of the global circuit for the shuffle is smaller with our solution: it contains less re-randomization / reencryption gates, O(N ) than the O(N log N ) re-randomization gates that would be required in this alternative solution.…”

Section: The Circuit That Encodes a Shufflementioning

confidence: 99%

Shorter Lattice-Based Zero-Knowledge Proofs for the Correctness of a Shuffle

Herranz

Martínez

Sánchez

2021

Lecture Notes in Computer Science

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In an electronic voting procedure, mixing networks are used to ensure anonymity of the casted votes. Each node of the network reencrypts 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 zeroknowledge argument for the correctness of a shuffle, for which we have mainly used two ideas: arithmetic circuit satisfiability results from [6] and Beneš networks to model a permutation of N elements. The achieved communication complexity of our protocol with respect to N is O( √ N log 2 (N )), but we will also highlight its dependency on other important parameters of the underlying lattice ingredients.

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Securing Abe’s Mix-Net Against Malicious Verifiers via Witness Indistinguishability

Cited by 7 publications

References 24 publications

YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model

YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model

(∈, δ)-Indistinguishable Mixing for Cryptocurrencies

Shorter Lattice-Based Zero-Knowledge Proofs for the Correctness of a Shuffle

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