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SNACKs for Proof-of-Space Blockchains

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Financial Cryptography and Data Security (FC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13951))

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Abstract

SNACKs are succinct non-interactive arguments of chain knowledge. They allow for efficient and generic solutions to blockchain light-client bootstrapping. Abusalah et al. construct SNACKs in the random oracle model for any single-chain blockchain from any graph-labeling proof of sequential work (PoSW) scheme. Their SNACK construction is a PoSW-like protocol over the augmented blockchain.

Unlike single-chain blockchains, such as proof-of-work and proof-of-stake blockchains, proof-of-space (PoSpace) blockchains are composed of two chains: a canonical proof chain and a data chain. These two chains are related using a signature scheme.

In this work, we construct PoSW-enabled SNACKs for any PoSpace blockchain. Combined with the results of Abusalah et al., this gives the first solution to light-client bootstrapping in PoSpace blockchains. The space cost of our construction is two hash values in each augmented PoSpace block. Generating SNACK proofs for a PoSpace blockchain is identical to generating SNACK proofs for single-chain blockchains and amounts to looking up a succinct number of augmented blocks.

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Notes

  1. 1.

    This assumption was first introduced in [6] in the PoW-blockchain setting and adopted in [3] generically, i.e., without reference to the Sybil-mechanism of the underlying blockchain protocol. Studying the \((c,\ell ,\epsilon )\)-fork assumption in various blockchain protocols, and possibly deriving it from their underlying security assumptions, is an interesting open problem that we don’t address in this work.

  2. 2.

    Depending on the PoSW scheme used, this number maybe \(O(t\log n)\) where n is the length of the blockchain and t a security parameter.

  3. 3.

    SNACKs are on par with Flyclient in terms of practical efficiency [3].

  4. 4.

    In fact, in Chia, the pair \((\textsf{VDF}_v^i,\textsf{VDF}_p^i)\) is a pair of tuples, i.e., \(\textsf{VDF}_v^i=(y_{i_1},\ldots , y_{i_k})\) and \(\textsf{VDF}_p^i=(\rho _{i_1},\ldots , \rho _{i_k})\) where \((y_{i_j},\rho _{i_j})\) is a VDF evaluation/proof pair on a challenge and time parameter pair \((x_{i_j},t_{i_j})\), which is uniquely defined by the proof chain so far \((c_{0},\ldots ,c_{i-1})\).

  5. 5.

    In the full version, we highlight the need for canonical proofs in PoSpace blockchains.

  6. 6.

    We remark that all PoSW schemes in the ROM [2,3,4, 7, 9, 11] use deterministic \(\textsf{Com}\) anyway.

  7. 7.

    A SNACK is a succinct and non-interactive ACK.

References

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Acknowledgements

I want to thank Karen Klein for a fruitful discussion at the beginning of the project and for her feedback on an early version of this paper. Parts of this work were done while the first author was at TUWien funded by the Vienna Science and Technology Fund (WWTF)[10.47379/VRG18002]. The project has also received funding in part from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under project PICOCRYPT (grant agreement No. 101001283), the Spanish Government under projects SCUM (ref. RTI2018-102043-B-I00), the Madrid Regional Government under project BLOQUES (ref. S2018/TCS-4339), and a research grant from Nomadic Labs and the Tezos Foundation.

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  1. IMDEA Software Institute, Madrid, Spain

    Hamza Abusalah

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  1. Hamza Abusalah
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Correspondence to Hamza Abusalah .

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Editors and Affiliations

  1. George Mason University, Fairfax, VA, USA

    Foteini Baldimtsi

  2. University of Bern, Bern, Switzerland

    Christian Cachin

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Abusalah, H. (2024). SNACKs for Proof-of-Space Blockchains. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13951. Springer, Cham. https://doi.org/10.1007/978-3-031-47751-5_1

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  • DOI: https://doi.org/10.1007/978-3-031-47751-5_1

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