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Our protocol consists of 3 setup messages and <jats:inline-formula><jats:alternatives><jats:tex-math>$$2N+1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mi>N<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> exchange messages and it is fair against covert adversaries with probability <jats:inline-formula><jats:alternatives><jats:tex-math>$$1- \\frac{1}{2N}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mfrac>\n                      <mml:mn>1<\/mml:mn>\n                      <mml:mrow>\n                        <mml:mn>2<\/mml:mn>\n                        <mml:mi>N<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:mfrac>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We prove that this is optimal up to shortening the setup phase which is notably more efficient than existing protocols.<\/jats:p>","DOI":"10.1007\/978-3-031-47754-6_6","type":"book-chapter","created":{"date-parts":[[2023,11,30]],"date-time":"2023-11-30T09:02:35Z","timestamp":1701334955000},"page":"94-111","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimally-Fair Exchange of\u00a0Secrets via\u00a0Delay Encryption and\u00a0Commutative Blinding"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7360-0143","authenticated-orcid":false,"given":"Ivo","family":"Maffei","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7557-3901","authenticated-orcid":false,"given":"Andrew W.","family":"Roscoe","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"6_CR1","doi-asserted-by":"crossref","unstructured":"Asokan, N., Schunter, M., Waidner, M.: Optimistic protocols for multi-party fair exchange. 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