{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:51:04Z","timestamp":1767340264600,"version":"3.41.2"},"reference-count":67,"publisher":"International Association for Cryptologic Research","license":[{"start":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T00:00:00Z","timestamp":1712620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IACR CiC"],"accepted":{"date-parts":[[2024,6,3]]},"abstract":" Distributed key generation (DKG) is a key building block in developing many efficient threshold cryptosystems. This work initiates the study of communication complexity and round complexity of DKG protocols over a point-to-point (bounded) synchronous network. Our key result is the first synchronous DKG protocol for discrete log-based cryptosystems with \n \n O<\/mml:mi>\n (<\/mml:mo>\n \u03ba<\/mml:mi>\n \n n<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> communication complexity (\n \n \u03ba<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math> denotes a security parameter) that tolerates any \n \n t<\/mml:mi>\n <<\/mml:mo>\n n<\/mml:mi>\n \/<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math> Byzantine faults among \n \n n<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math> parties. We present two variants of the protocol: (i) a protocol with worst-case \n \n O<\/mml:mi>\n (<\/mml:mo>\n \u03ba<\/mml:mi>\n \n n<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> communication and \n \n O<\/mml:mi>\n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> rounds, and (ii) a protocol with expected \n \n O<\/mml:mi>\n (<\/mml:mo>\n \u03ba<\/mml:mi>\n \n n<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> communication and expected constant rounds. In the process of achieving our results, we design (1) a novel weak gradecast protocol with a communication complexity of \n \n O<\/mml:mi>\n (<\/mml:mo>\n \u03ba<\/mml:mi>\n \n n<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> for linear-sized inputs and constant rounds, (2) a protocol called \u201crecoverable-set-of-shares\u201d for ensuring recovery of shared secrets, (3) an oblivious leader election protocol with \n \n O<\/mml:mi>\n (<\/mml:mo>\n \u03ba<\/mml:mi>\n \n n<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> communication and constant rounds, and (4) a multi-valued validated Byzantine agreement (MVBA) protocol with \n \n O<\/mml:mi>\n (<\/mml:mo>\n \u03ba<\/mml:mi>\n \n n<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math> communication complexity for linear-sized inputs and expected constant rounds. Each of these primitives is of independent interest. <\/jats:p>","DOI":"10.62056\/ayfhsgvtw","type":"journal-article","created":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T15:52:04Z","timestamp":1720453924000},"update-policy":"https:\/\/doi.org\/10.62056\/adfjwm02dj","source":"Crossref","is-referenced-by-count":3,"title":["Synchronous Distributed Key Generation without Broadcasts"],"prefix":"10.62056","author":[{"given":"Nibesh","family":"Shrestha","sequence":"first","affiliation":[{"name":"Supra Research","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adithya","family":"Bhat","sequence":"additional","affiliation":[{"name":"Visa Research","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aniket","family":"Kate","sequence":"additional","affiliation":[{"name":"Supra Research","place":["USA"]},{"name":"Purdue University","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kartik","family":"Nayak","sequence":"additional","affiliation":[{"name":"Duke University","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"48349","published-online":{"date-parts":[[2024,7,8]]},"reference":[{"key":"ref1:boldyreva2003threshold","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/3-540-36288-6_3","article-title":"Threshold Signatures, Multisignatures and Blind Signatures\n Based on the Gap-Diffie-Hellman-Group Signature Scheme","volume-title":"PKC\u00a02003: 6th International Workshop on Theory and Practice\n in Public Key Cryptography","volume":"2567","author":"Alexandra Boldyreva","year":"2003"},{"key":"ref2:shoup2000practical","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/3-540-45539-6_15","article-title":"Practical Threshold Signatures","volume-title":"Advances in Cryptology \u2013 EUROCRYPT\u00a02000","volume":"1807","author":"Victor Shoup","year":"2000"},{"key":"ref3:DesmedtF89","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/0-387-34805-0_28","article-title":"Threshold Cryptosystems","volume-title":"Advances in Cryptology \u2013 CRYPTO'89","volume":"435","author":"Yvo Desmedt","year":"1990"},{"journal-title":"GitHub","article-title":"Drand - A Distributed Randomness Beacon Daemon","author":"Drand","key":"ref4:drand"},{"key":"ref5:cachin2005random","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1145\/343477.343531","article-title":"Random oracles in constantipole: practical asynchronous\n Byzantine agreement using cryptography (extended abstract)","volume-title":"19th ACM Symposium Annual on Principles of Distributed\n Computing","author":"Christian Cachin","year":"2000"},{"key":"ref6:yin2019hotstuff","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1145\/3293611.3331591","article-title":"HotStuff: BFT Consensus with Linearity and\n Responsiveness","volume-title":"38th ACM Symposium Annual on Principles of Distributed\n Computing","author":"Maofan Yin","year":"2019"},{"key":"ref7:shrestha2020optimality","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1145\/3372297.3417284","article-title":"On the Optimality of Optimistic Responsiveness","volume-title":"ACM CCS 2020: 27th Conference on Computer and Communications\n Security","author":"Nibesh Shrestha","year":"2020"},{"key":"ref8:hirt2005cryptographic","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1007\/11426639_19","article-title":"Cryptographic Asynchronous Multi-party Computation with\n Optimal Resilience (Extended Abstract)","volume-title":"Advances in Cryptology \u2013 EUROCRYPT\u00a02005","volume":"3494","author":"Martin Hirt","year":"2005"},{"key":"ref9:hofheinz2004synchronous","article-title":"A Synchronous Model for Multi-Party Computation and the\n Incompleteness of Oblivious Transfer","author":"Dennis Hofheinz","year":"2004","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"ref10:distributedKDC","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1007\/3-540-36178-2_22","article-title":"On Unconditionally Secure Robust Distributed Key\n Distribution Centers","volume-title":"Advances in Cryptology \u2013 ASIACRYPT\u00a02002","volume":"2501","author":"Paolo D'Arco","year":"2002"},{"article-title":"Torus: Globally accessible public key infrastructure for\n everyone","year":"2021","author":"Torus Lab","key":"ref11:Torus"},{"key":"ref12:pedersendkg","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1007\/3-540-46416-6_47","article-title":"A Threshold Cryptosystem without a Trusted Party","volume-title":"Advances in Cryptology \u2013 EUROCRYPT'91","volume":"547","author":"Torben P. 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