Abstract
An aggregatable subvector commitment (aSVC) scheme is a vector commitment (VC) scheme that can aggregate multiple proofs into a single, small subvector proof. In this paper, we formalize aSVCs and give a construction from constant-sized polynomial commitments. Our construction is unique in that it has linear-sized public parameters, it can compute all constant-sized proofs in quasilinear time, it updates proofs in constant time and it can aggregate multiple proofs into a constant-sized subvector proof. Furthermore, our concrete proof sizes are small due to our use of pairing-friendly groups. We use our aSVC to obtain a payments-only stateless cryptocurrency with very low communication and computation overheads. Specifically, our constant-sized, aggregatable proofs reduce each block’s proof overhead to a single group element, which is optimal. Furthermore, our subvector proofs speed up block verification and our smaller public parameters further reduce block size.
An errata for this paper can be found at https://github.com/alinush/asvc-paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptol. 21(2), 149–177 (2007). https://doi.org/10.1007/s00145-007-9005-7
Boneh, D., Bünz, B., Fisch, B.: Batching techniques for accumulators with applications to IOPs and stateless blockchains. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 561–586. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_20
Bowe, S., Gabizon, A., Miers, I.: Scalable multi-party computation for zk-SNARK parameters in the random beacon model (2017). https://eprint.iacr.org/2017/1050
Bonneau, J., Meckler, I., Rao, V., Shapiro, E.: Coda: Decentralized Cryptocurrency at Scale (2020). https://eprint.iacr.org/2020/352
Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M.: Scalable zero knowledge via cycles of elliptic curves. Algorithmica 79(4), 1102–1160 (2016). https://doi.org/10.1007/s00453-016-0221-0
Buterin, V.: The stateless client concept. ethresear.ch (2017). https://ethresear.ch/t/ the-stateless-client-concept/172
Buterin, V.: Using polynomial commitments to replace state roots (2020). https://ethresear.ch/t/using-polynomial-commitments-to-replace-state-roots/7095
Camenisch, J., Dubovitskaya, M., Haralambiev, K., Kohlweiss, M.: Composable and modular anonymous credentials: definitions and practical constructions. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 262–288. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48800-3_11
Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 55–72. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_5
Campanelli, M., Fiore, D., Greco, N., Kolonelos, D., Nizzardo, L.: Vector Commitment Techniques and Applications to Verifiable Decentralized Storage (2020). https://eprint.iacr.org/2020/149
Catalano, D., Fiore, D., Messina, M.: Zero-knowledge sets with short proofs. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 433–450. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_25
Chepurnoy, A., Papamanthou, C., Zhang, Y.: Edrax: A Cryptocurrency with Stateless Transaction Validation (2018). https://eprint.iacr.org/2018/968
Dryja, T.: Utreexo: A dynamic hash-based accumulator optimized for the Bitcoin UTXO set (2019). https://eprint.iacr.org/2019/611
Feist, D., Khovratovich, D.: Fast amortized Kate proofs (2020). https://github.com/khovratovich/Kate
Goyal, V.: Reducing trust in the PKG in identity based cryptosystems. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 430–447. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_24
Gorbunov, S., Reyzin, L., Wee, H., Zhang, Z.: Pointproofs: Aggregating Proofs for Multiple Vector Commitments (2020). https://eprint.iacr.org/2020/419
Kokoris-Kogias, E., Jovanovic, P., Gasser, L., Gailly, N., Syta, E., Ford, B.: OmniLedger: a secure, scale-out, decentralized ledger via sharding. In: IEEE S&P 2018, May 2018
Kohlweiss, M., Rial, A.: Optimally private access control. In: ACM WPES 2013 (2013)
Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_11
Lai, R.W.F., Malavolta, G.: Subvector commitments with application to succinct arguments. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 530–560. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_19
Libert, B., Yung, M.: Concise mercurial vector commitments and independent zero-knowledge sets with short proofs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 499–517. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_30
Miller, A.: Storing UTXOs in a balanced Merkle tree (zero-trust nodes with O(1)-storage) (2012). https://bitcointalk.org/index.php?topic=101734.msg1117428
Nakamoto, S.: Bitcoin: A Peer-to-Peer Electronic Cash System (2008). https://bitcoin.org/bitcoin.pdf
Papamanthou, C., Shi, E., Tamassia, R.: Signatures of correct computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 222–242. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_13
Reyzin, L., Meshkov, D., Chepurnoy, A., Ivanov, S.: Improving authenticated dynamic dictionaries, with applications to cryptocurrencies. In: Kiayias, A. (ed.) FC 2017. LNCS, vol. 10322, pp. 376–392. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70972-7_21
Tomescu, A., Abraham, I., Buterin, V., Drake, J., Feist, D., Khovratovich, D.: Aggregatable Subvector Commitments for Stateless Cryptocurrencies (2020). https://eprint.iacr.org/2020/527
Todd, P.: Making UTXO set growth irrelevant with low-latency delayed TXO commitments (2016). https://petertodd.org/2016/delayed-txo-commitments
Tomescu, A.: How to Keep a Secret and Share a Public Key (Using Polynomial Commitments). PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, USA (2020)
Virza, M.: On Deploying Succinct Zero-Knowledge Proofs. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, USA (2017)
von zur Gathen, J., Gerhard, J.: Fast multiplication. In: Modern Computer Algebra, 3rd edn, chapter 8, pp. 221–254. Cambridge University Press, Cambridge (2013)
von zur Gathen, J., Gerhard, J.: Fast polynomial evaluation and interpolation. In: Modern Computer Algebra, 3rd edn, chapter 10, pp. 295–310. Cambridge University Press, Cambridge (2013)
Wood, G.: Ethereum: A Secure Decentralised Generalised Transaction Ledger (2014). http://gavwood.com/paper.pdf
Acknowledgements
The authors want to thank Madars Virza for pointing out the Lagrange-based approach to VCs and the DFT technique for computing all KZG commitments to Lagrange polynomials. We also thank Leonid Reyzin and Dimitris Kolonelos for corrections and productive conversations that helped improve this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Tomescu, A., Abraham, I., Buterin, V., Drake, J., Feist, D., Khovratovich, D. (2020). Aggregatable Subvector Commitments for Stateless Cryptocurrencies. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-57990-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57989-0
Online ISBN: 978-3-030-57990-6
eBook Packages: Computer ScienceComputer Science (R0)