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

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13791))

Abstract

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 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 encryption scheme.

I. Cascudo—Supported by the Spanish Government under the project SecuRing (ref. PID2019-110873RJ-I00/MCIN/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.

B. David—Supported by the Concordium Foundation and by the Independent Research Fund Denmark (IRFD) grants number 9040-00399B (TrA2C), 9131-00075B (PUMA) and 0165-00079B.

L. Garms—Supported by a research grant from Nomadic Labs and the Tezos Foundation.

A. Konring—Supported by the IRFD grant number 9040-00399B (TrA2C).

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Notes

  1. 1.

    This extends to direct products of groups of order p, i.e. \(\mathcal {W}=\mathbb {G}_1\times \dots \times \mathbb {G}_m\), \(\mathcal {X}=\mathbb {G}_1'\times \dots \times \mathbb {G}'_n\) and \(f=(f_1,\dots ,f_m):\mathcal {W}\rightarrow \mathcal {X}\) where \(f_i:\mathbb {G}_i\rightarrow \mathcal {X}\) are all group homomorphisms.

  2. 2.

    Specifically from the fact that the dual of a Reed-Solomon code is a generalized Reed-Solomon code of a certain form.

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Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Ignacio Cascudo & Lydia Garms

  2. IT University of Copenhagen, Copenhagen, Denmark

    Bernardo David & Anders Konring

  3. Keyless Technologies Limited, London, UK

    Lydia Garms

Authors
  1. Ignacio Cascudo
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  2. Bernardo David
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  3. Lydia Garms
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  4. Anders Konring
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Corresponding author

Correspondence to Ignacio Cascudo .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Cascudo, I., David, B., Garms, L., Konring, A. (2022). YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_22

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  • DOI: https://doi.org/10.1007/978-3-031-22963-3_22

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