Abstract
The decentralization of the blockchain has led to the leakage of privacy data at the transaction layer, causing information security issues. The zero-knowledge range proof can confidentially verify that the transaction amount belongs to a legal positive integer range without revealing the transaction, effectively solving the privacy leakage of the blockchain transaction layer. The currently known blockchain range proof scheme is unable to process floating-point numbers, which limits the application fields of range proof. Moreover, the existing solutions can be further optimized in terms of proof speed, verification speed, and computational cost. We propose Ferproof, a constant cost range proof with floating-point number adaptation. Ferproof improves the zero-knowledge protocol based on Bulletproofs to optimize the proof structure, and a Lagrangian inner product vector generation method is issued to make the witness generation time constant and the commitment is constructed according to the floating-point number range relationship to implement floating-point range proof. Ferproof only relies on the discrete logarithm assumption, and the third-party credibility is not required. The communication cost and time complexity of Ferproof are constant. According to the experimental results, compared with the most advanced known range proof scheme, Ferproof’s proof speed is increased by 40.0%, and the verification speed is increased by 29.8%.
Supported by organization Key Research and Development Program Project of Ministry of Science and Technology (No. 2019YFD1101104).
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References
Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system[EB/OL]. SSRN Electron. J. (2008). https://bitcoin.org/bitcoin.pdf
Bonneau, J., Miller, A., Clark, J., Narayanan, A., Kroll, J.A., et al.: Research perspectives and challenges for bitcoin and cryptocurrencies, pp. 104–121. IEEE (2015)
Liu, M., Chen, Z., Shi, Y., Tang, L., Cao, D.: Research progress of blockchain in data security. Chin. J. Comput. 44(1), 1–27 (2021)
Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. J. Cryptol. 7(1), 1–32 (1994). https://doi.org/10.1007/BF00195207
Maxwell, G.: Confidential transactions (2016). https://people.xiph.org/greg/confidential_values.txt
Blum, M.: Coin flipping by telephone. In: Advances in Cryptology: A Report on CRYPTO 81, CRYPTO 81, IEEE Workshop on Communications Security, pp. 11–15 (1981)
Maxwell, G., Poelstra, A.: Borromean ring signatures [EB/OL] (2015). http://diyhpl.us/bryan/papers2/bitcoin/Borromean%20ring%20signatures.pdf
Noether, S.: Ring signature confidential transactions for Monero. IACR Cryptology ePrint Achieve (2015). https://eprint.iacr.org/2015/1_098.pdf
Sun, S.-F., Au, M.H., Liu, J.K., Yuen, T.H.: RingCT 2.0: a compact accumulator-based (linkable ring signature) protocol for blockchain cryptocurrency Monero. In: Foley, S.N., Gollmann, D., Snekkenes, E. (eds.) ESORICS 2017. LNCS, vol. 10493, pp. 456–474. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66399-9_25
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_9
Wood, G.: Ethereum: a secure decentralised transaction ledger [EB/OL] (2014). http://gavwood.com/paper.pdf
McCorry, P., Shahandashti, S.F., Hao, F.: A smart contract for boardroom voting with maximum voter privacy. In: Kiayias, A. (ed.) FC 2017. LNCS, vol. 10322, pp. 357–375. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70972-7_20
Campanelli, M., Gennaro, R., Goldfeder, S., Nizzardo, L.: Zero-knowledge contingent payments revisited: attacks and payments for services. In: Conference on Computer and Communications Security. ACM (2017)
Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: Proceedings of the 34th IEEE Symposium on Security and Privacy, pp. 238–252. IEEE (2013)
Ben-Sasson, E., Chiesa, A., Genkin, D., Tromer, E., Virza, M.: SNARKs for C: verifying program executions succinctly and in zero knowledge. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 90–108. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_6
Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. Commun. ACM 59, 103–112 (2016)
Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 305–326. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_11
Peterson, P.: Zcash-transaction linkability [EB/OL], 25 January 2017. https://z.cash/_blog/transaction-linkability.html
Wahby, R.S., Tzialla, I., Shelat, A., Thaler, J., Walfish, M.: Doubly-efficient zkSNARKs without trusted setup. In: Proceedings of 2018 IEEE Symposium on Security and Privacy (SP), pp. 2375–1207. IEEE (2018)
Setty, S., Angel, S., Lee, J.: Verifiable state machines: proofs that untrusted services operate correctly. ACM SIGOPS Oper. Syst. Rev. 54(1), 40–46 (2020)
Ben-Sasson, E., Bentov, I., Horesh, Y., Riabzev, M.: Scalable, transparent, and post-quantum secure computational integrity. IACR Cryptology ePrint Archive, 2018:46 (2018)
Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge snarks from linear-size universal and updatable structured reference strings. Cryptology ePrint Archive (2019)
Gabizon, A., Williamson, Z.J., Ciobotaru, O.: PLONK: permutations over lagrange-bases for Oecumenical noninteractive arguments of knowledge. Cryptology ePrint Archive, 2019:953 (2019)
Lipmaa, H.: On Diophantine complexity and statistical zero-knowledge arguments. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 398–415. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40061-5_26
Groth, J.: Non-interactive zero-knowledge arguments for voting. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 467–482. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_32
Bünz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell, G.: Bulletproofs: short proofs for confidential transactions and more. In: 2018 IEEE Symposium on Security and Privacy (SP), pp. 315–334. IEEE (2018)
Bootle, J., Cerulli, A., Chaidos, P., Groth, J., Petit, C.: Efficient zero-knowledge arguments for arithmetic circuits in the discrete log setting. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 327–357. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_12
Deng, C., Tang, X., et al.: Cuproof: a novel range proof with constant size. IACR Cryptology e Print Achieve (2021)
Feige, U., Fiat, A., Shamir, A.: Zero-knowledge proofs of identity. J. Cryptol. 1(2), 77–94 (1988). https://doi.org/10.1007/BF02351717
Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)
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Li, Y., Zhou, K., Xu, L., Wang, M., Liu, N. (2022). Ferproof: A Constant Cost Range Proof Suitable for Floating-Point Numbers. In: Lai, Y., Wang, T., Jiang, M., Xu, G., Liang, W., Castiglione, A. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2021. Lecture Notes in Computer Science(), vol 13157. Springer, Cham. https://doi.org/10.1007/978-3-030-95391-1_41
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