{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T15:59:30Z","timestamp":1783007970126,"version":"3.54.5"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"publisher","award":["13\/RC\/2106"],"award-info":[{"award-number":["13\/RC\/2106"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"publisher","award":["17\/SP\/5447"],"award-info":[{"award-number":["17\/SP\/5447"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>The evolution of smart contracts in recent years inspired a crucial question: do smart contract evaluation protocols provide the required level of privacy when executing contracts on the blockchain? The Hawk (IEEE S&amp;P \u201916) paper introduces a way to solve the problem of privacy in smart contracts by evaluating the contracts off-chain, albeit with the trust assumption of a manager. To avoid the partially trusted manager altogether, a novel approach named zkHawk (IEEE BRAINS \u201921) explains how we can evaluate the contracts privately off-chain using a multi-party computation (MPC) protocol instead of trusting said manager. This paper dives deeper into the detailed construction of a variant of the zkHawk protocol titled V-zkHawk using formal proofs to construct the said protocol and model its security in the universal composability (UC) framework (FOCS \u201901). The V-zkHawk protocol discussed here does not support immediate closure, i.e., all the parties (n) have to send a message to inform the blockchain that the contract has been executed with corruption allowed for up to t parties, where t&lt;n. In the most quintessential sense, the V-zkHawk is a variant because the outcome of the protocol is similar (i.e., execution of smart contract via an MPC function evaluation) to zkHawk, but we modify key aspects of the protocol, essentially creating a small trade-off (removing immediate closure) to provide UC (stronger) security. The V-zkHawk protocol leverages joint Schnorr signature schemes, encryption schemes, Non-Interactive Zero-Knowledge Proofs (NIZKs), and commitment schemes with Common Reference String (CRS) assumptions, MPC function evaluations, and assumes the existence of asynchronous, authenticated broadcast channels. We achieve malicious security in a dishonest majority setting in the UC framework.<\/jats:p>","DOI":"10.3390\/cryptography6030039","type":"journal-article","created":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T21:52:48Z","timestamp":1659649968000},"page":"39","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multiverse of HawkNess: A Universally-Composable MPC-Based Hawk Variant"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6081-9374","authenticated-orcid":false,"given":"Aritra","family":"Banerjee","sequence":"first","affiliation":[{"name":"ADAPT Centre, Trinity College Dublin, D02 PN40 Dublin, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1738-527X","authenticated-orcid":false,"given":"Hitesh","family":"Tewari","sequence":"additional","affiliation":[{"name":"ADAPT Centre, Trinity College Dublin, D02 PN40 Dublin, Ireland"},{"name":"School of Computer Science and Statistics, Trinity College Dublin, D02 R123 Dublin, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1080\/13600834.2017.1301036","article-title":"Contract law 2.0:\u2018Smart\u2019contracts as the beginning of the end of classic contract law","volume":"26","author":"Savelyev","year":"2017","journal-title":"Inf. Commun. Technol. Law"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Buterin, V. (2022, June 23). A Next Generation Smart Contract & Decentralized Application Platform (2013) Whitepaper. Ethereum Foundation. Available online: https:\/\/blockchainlab.com\/pdf\/Ethereum_white_paper-a_next_generation_smart_contract_and_decentralized_application_platform-vitalik-buterin.pdf.","DOI":"10.1109\/ICSES55317.2022.9914151"},{"key":"ref_3","unstructured":"Sasson, E.B., Chiesa, A., Garman, C., Green, M., Miers, I., Tromer, E., and Virza, M. (2014, January 18\u201321). Zerocash: Decentralized anonymous payments from bitcoin. Proceedings of the 2014 IEEE Symposium on Security and Privacy, Berkeley, CA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Groth, J. (2016). On the size of pairing-based non-interactive arguments. Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer.","DOI":"10.1007\/978-3-662-49896-5_11"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Groth, J. (2010). Short pairing-based non-interactive zero-knowledge arguments. International Conference on the Theory and Application of Cryptology and Information Security, Springer.","DOI":"10.1007\/978-3-642-17373-8_19"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Banerjee, A., Clear, M., and Tewari, H. (2020, January 17\u201319). Demystifying the Role of zk-SNARKs in Zcash. Proceedings of the 2020 IEEE Conference on Application, Information and Network Security (AINS), Kota Kinabalu, Malaysia.","DOI":"10.1109\/AINS50155.2020.9315064"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kosba, A., Miller, A., Shi, E., Wen, Z., and Papamanthou, C. (2016, January 22\u201326). Hawk: The blockchain model of cryptography and privacy-preserving smart contracts. Proceedings of the 2016 IEEE symposium on security and privacy (SP), San Jose, CA, USA.","DOI":"10.1109\/SP.2016.55"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Banerjee, A., Clear, M., and Tewari, H. (2021). zkHawk: Practical Private Smart Contracts from MPC-based Hawk. arXiv.","DOI":"10.1109\/BRAINS52497.2021.9569822"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kursawe, K., Danezis, G., and Kohlweiss, M. (2011). Privacy-friendly aggregation for the smart-grid. Privacy Enhancing Technologies, Springer.","DOI":"10.1007\/978-3-642-22263-4_10"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Keller, M. (2020, January 9\u201313). MP-SPDZ: A versatile framework for multi-party computation. Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security, Virtual.","DOI":"10.1145\/3372297.3417872"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yao, A.C. (1982, January 3\u20135). Protocols for secure computations. Proceedings of the 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982), Chicago, IL, USA.","DOI":"10.1109\/SFCS.1982.38"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Micali, S., Goldreich, O., and Wigderson, A. (1987, January 1). How to play any mental game. Proceedings of the Nineteenth ACM Symposium on Theory of Computing, STOC, ACM, New York, NY, USA.","DOI":"10.1145\/28395.28420"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bogetoft, P., Christensen, D.L., Damg\u00e5rd, I., Geisler, M., Jakobsen, T., Kr\u00f8igaard, M., Nielsen, J.D., Nielsen, J.B., Nielsen, K., and Pagter, J. (2009). Secure multiparty computation goes live. International Conference on Financial Cryptography and Data Security, Springer.","DOI":"10.1007\/978-3-642-03549-4_20"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Damg\u00e5rd, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., and Smart, N.P. (2013). Practical covertly secure MPC for dishonest majority\u2013or: Breaking the SPDZ limits. European Symposium on Research in Computer Security, Springer.","DOI":"10.1007\/978-3-642-40203-6_1"},{"key":"ref_15","first-page":"1749","article-title":"From keys to databases\u2014Real-world applications of secure multi-party computation","volume":"61","author":"Archer","year":"2018","journal-title":"Comput. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Boyle, E., Gilboa, N., and Ishai, Y. (2015). Function secret sharing. Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer.","DOI":"10.1007\/978-3-662-46803-6_12"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Canetti, R. (2001, January 8\u201311). Universally composable security: A new paradigm for cryptographic protocols. Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, Newport Beach, CA, USA.","DOI":"10.1109\/SFCS.2001.959888"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Canetti, R., and Fischlin, M. (2001). Universally composable commitments. Annual International Cryptology Conference, Springer.","DOI":"10.1007\/3-540-44647-8_2"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Blum, M., Feldman, P., and Micali, S. (2019). Non-interactive zero-knowledge and its applications. Providing Sound Foundations for Cryptography: On the Work of Shafi Goldwasser and Silvio Micali, ACM.","DOI":"10.1145\/3335741.3335757"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Banerjee, A. (2021). A Fully Anonymous e-Voting Protocol Employing Universal Zk-SNARKs and Smart Contracts. International Congress on Blockchain and Applications, Springer.","DOI":"10.1007\/978-3-030-86162-9_35"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Steffen, S., Bichsel, B., Gersbach, M., Melchior, N., Tsankov, P., and Vechev, M. (2019, January 11\u201315). zkay: Specifying and enforcing data privacy in smart contracts. Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, London, UK.","DOI":"10.1145\/3319535.3363222"},{"key":"ref_22","unstructured":"Kalodner, H., Goldfeder, S., Chen, X., Weinberg, S.M., and Felten, E.W. (2018, January 15\u201317). Arbitrum: Scalable, private smart contracts. Proceedings of the 27th {USENIX} Security Symposium ({USENIX} Security 18), Baltimore, MD, USA."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kerber, T., Kiayias, A., and Kohlweiss, M. (2021, January 21\u201324). KACHINA\u2013Foundations of Private Smart Contracts. Proceedings of the 2021 IEEE 34th Computer Security Foundations Symposium (CSF), IEEE, Dubrovnik, Croatia.","DOI":"10.1109\/CSF51468.2021.00002"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"B\u00fcnz, B., Agrawal, S., Zamani, M., and Boneh, D. (2020). Zether: Towards privacy in a smart contract world. International Conference on Financial Cryptography and Data Security, Springer.","DOI":"10.1007\/978-3-030-51280-4_23"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Botta, V., Friolo, D., Venturi, D., and Visconti, I. (2021, January 1\u20135). Shielded computations in smart contracts overcoming forks. Proceedings of the International Conference on Financial Cryptography and Data Security, Virtual Event.","DOI":"10.1007\/978-3-662-64322-8_4"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1007\/s11390-018-1839-y","article-title":"Shadoweth: Private smart contract on public blockchain","volume":"33","author":"Yuan","year":"2018","journal-title":"J. Comput. Sci. Technol."},{"key":"ref_27","first-page":"1","article-title":"Intel sgx explained","volume":"2016","author":"Costan","year":"2016","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Canetti, R., Dodis, Y., Pass, R., and Walfish, S. (2007). Universally composable security with global setup. Theory of Cryptography Conference, Springer.","DOI":"10.1007\/978-3-540-70936-7_4"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Badertscher, C., Canetti, R., Hesse, J., Tackmann, B., and Zikas, V. (2020). Universal composition with global subroutines: Capturing global setup within plain UC. Theory of Cryptography Conference, Springer.","DOI":"10.1007\/978-3-030-64381-2_1"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S0097539792230010","article-title":"Multiple noninteractive zero knowledge proofs under general assumptions","volume":"29","author":"Feige","year":"1999","journal-title":"SIAM J. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2220357.2220358","article-title":"New techniques for noninteractive zero-knowledge","volume":"59","author":"Groth","year":"2012","journal-title":"J. ACM (JACM)"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., and Waters, B. (2006). Sequential aggregate signatures and multisignatures without random oracles. Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer.","DOI":"10.1007\/11761679_28"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2139","DOI":"10.1007\/s10623-019-00608-x","article-title":"Simple Schnorr multi-signatures with applications to Bitcoin","volume":"87","author":"Maxwell","year":"2019","journal-title":"Des. Codes Cryptogr."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Boneh, D., Lynn, B., and Shacham, H. (2001). Short signatures from the Weil pairing. International Conference on the Theory and Application of Cryptology and Information Security, Springer.","DOI":"10.1007\/3-540-45682-1_30"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Boneh, D., Gentry, C., Lynn, B., and Shacham, H. (2003). Aggregate and verifiably encrypted signatures from bilinear maps. International Conference on the Theory and Applications of Cryptographic Techniques, Springer.","DOI":"10.1007\/3-540-39200-9_26"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s102070100002","article-title":"The elliptic curve digital signature algorithm (ECDSA)","volume":"1","author":"Johnson","year":"2001","journal-title":"Int. J. Inf. Secur."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1007\/s10623-018-0535-9","article-title":"Key-homomorphic signatures: Definitions and applications to multiparty signatures and non-interactive zero-knowledge","volume":"87","author":"Derler","year":"2019","journal-title":"Des. Codes Cryptogr."},{"key":"ref_38","unstructured":"Canetti, R. (2022, June 23). Security and Composition of Cryptographic Protocols: A Tutorial. Cryptology ePrint Archive, Report 2006\/465. Available online: https:\/\/ia.cr\/2006\/465."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Canetti, R., Lindell, Y., Ostrovsky, R., and Sahai, A. (2002, January 19\u201321). Universally composable two-party and multi-party secure computation. Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, Montreal, QC, Canada.","DOI":"10.1145\/509907.509980"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Li, Q., Cascudo, I., and Christensen, M.G. (2019, January 2\u20136). Privacy-preserving distributed average consensus based on additive secret sharing. Proceedings of the 2019 27th European Signal Processing Conference (EUSIPCO), A Coruna, Spain.","DOI":"10.23919\/EUSIPCO.2019.8902577"},{"key":"ref_41","unstructured":"Krawczyk, H. (1993). Secret sharing made short. Annual International Cryptology Conference, Springer."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Damg\u00e5rd, I., Geisler, M., Kr\u00f8igaard, M., and Nielsen, J.B. (2009). Asynchronous multiparty computation: Theory and implementation. International Workshop on Public Key Cryptography, Springer.","DOI":"10.1007\/978-3-642-00468-1_10"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s00145-005-0319-z","article-title":"Secure multi-party computation without agreement","volume":"18","author":"Goldwasser","year":"2005","journal-title":"J. Cryptol."},{"key":"ref_44","unstructured":"Pedersen, T.P. (1991). Non-interactive and information-theoretic secure verifiable secret sharing. Annual International Cryptology Conference, Springer."},{"key":"ref_45","unstructured":"Canetti, R. (2004, January 30). Universally composable signature, certification, and authentication. Proceedings of the 17th IEEE Computer Security Foundations Workshop, Pacific Grove, CA, USA."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Boneh, D., Drijvers, M., and Neven, G. (2018). Compact multi-signatures for smaller blockchains. International Conference on the Theory and Application of Cryptology and Information Security, Springer.","DOI":"10.1007\/978-3-030-03329-3_15"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Laud, P., and Kamm, L. (2015). Applications of Secure Multiparty Computation, IOS Press.","DOI":"10.1515\/popets-2015-0011"},{"key":"ref_48","unstructured":"Damg\u00e5rd, I., Ravi, D., Siniscalchi, L., and Yakoubov, S. (2022, June 23). Minimizing Setup in Broadcast-Optimal Two Round MPC. Cryptology ePrint Archive, Report 2022\/293. Available online: https:\/\/ia.cr\/2022\/293."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Cohen, R., Garay, J., and Zikas, V. (2020). Broadcast-optimal two-round MPC. Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer.","DOI":"10.1007\/978-3-030-45724-2_28"},{"key":"ref_50","unstructured":"Ciampi, M., Ostrovsky, R., Waldner, H., and Zikas, V. (2022, June 23). Round-Optimal and Communication-Efficient Multiparty Computation. Cryptology ePrint Archive, Report 2020\/1437. Available online: https:\/\/ia.cr\/2020\/1437."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Garg, S., and Polychroniadou, A. (2015). Two-round adaptively secure MPC from indistinguishability obfuscation. Theory of Cryptography Conference, Springer.","DOI":"10.1007\/978-3-662-46497-7_24"}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/6\/3\/39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:04:21Z","timestamp":1760141061000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/6\/3\/39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,4]]},"references-count":51,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["cryptography6030039"],"URL":"https:\/\/doi.org\/10.3390\/cryptography6030039","relation":{},"ISSN":["2410-387X"],"issn-type":[{"value":"2410-387X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,4]]}}}