{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T05:11:48Z","timestamp":1750137108820,"version":"3.37.3"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T00:00:00Z","timestamp":1720569600000},"content-version":"vor","delay-in-days":9,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002744","name":"Bar-Ilan University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002744","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Cryptol"],"published-print":{"date-parts":[[2024,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct the first actively-secure Multi-Party Computation (MPC) protocols with an <jats:italic>arbitrary<\/jats:italic> number of parties in the dishonest majority setting, for an <jats:italic>arbitrary<\/jats:italic> field <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {F}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>F<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with <jats:italic>constant communication overhead<\/jats:italic> over the \u201cpassive-GMW\u201d protocol (Goldreich, Micali and Wigderson, STOC \u201887). Our protocols rely on passive implementations of Oblivious Transfer (OT) in the Boolean setting and Oblivious Linear function Evaluation (OLE) in the arithmetic setting. Previously, such protocols were only known over sufficiently large fields (Genkin et al. STOC \u201814) or a constant number of parties (Ishai et al. CRYPTO \u201808). Conceptually, our protocols are obtained via a new compiler from a passively-secure protocol for a distributed multiplication functionality <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {F}}}}_{\\scriptscriptstyle \\textrm{MULT}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mstyle>\n                      <mml:mtext>MULT<\/mml:mtext>\n                    <\/mml:mstyle>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, to an actively-secure protocol for general functionalities. Roughly, <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {F}}}}_{\\scriptscriptstyle \\textrm{MULT}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mstyle>\n                      <mml:mtext>MULT<\/mml:mtext>\n                    <\/mml:mstyle>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is parameterized by a linear-secret sharing scheme <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {S}}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>S<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where it takes <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {S}}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>S<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-shares of two secrets and returns <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {S}}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>S<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-shares of their product. We show that our compilation is concretely efficient for sufficiently large fields, resulting in an overhead of 2 when securely computing natural circuits. Our compiler has two additional benefits: (1) It can rely on <jats:italic>any<\/jats:italic> passive implementation of <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {F}}}}_{\\scriptscriptstyle \\textrm{MULT}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mstyle>\n                      <mml:mtext>MULT<\/mml:mtext>\n                    <\/mml:mstyle>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which, besides the standard implementation based on OT (for Boolean) and OLE (for arithmetic), allows us to rely on implementations based on threshold cryptosystems (Cramer et al. Eurocrypt \u201801), and (2) it can rely on weaker-than-passive (i.e., imperfect\/leaky) implementations, which in some parameter regimes yield actively-secure protocols with overhead less than 2. Instantiating this compiler with an \u201chonest-majority\u201d implementation of <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {F}}}}_{\\scriptscriptstyle \\textrm{MULT}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mstyle>\n                      <mml:mtext>MULT<\/mml:mtext>\n                    <\/mml:mstyle>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we obtain the first honest-majority protocol (with up to one-third corruptions) for Boolean circuits with constant communication overhead over the best passive protocol (Damg\u00e5rd and Nielsen, CRYPTO \u201807). \n<\/jats:p>","DOI":"10.1007\/s00145-024-09509-2","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T00:06:16Z","timestamp":1720569976000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Price of Active Security in Cryptographic Protocols"],"prefix":"10.1007","volume":"37","author":[{"given":"Carmit","family":"Hazay","sequence":"first","affiliation":[]},{"given":"Muthuramakrishnan","family":"Venkitasubramaniam","sequence":"additional","affiliation":[]},{"given":"Mor","family":"Weiss","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"9509_CR1","doi-asserted-by":"crossref","unstructured":"B. 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