乐胖代购免代理版

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$$f$$<\/jats:tex-math>\n f<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> on a hidden input to obtain a hidden output, without the executer learning anything about either of the two (e.g., [12]). We explore the case where

$$f$$<\/jats:tex-math>\n f<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> implements a universal function, i.e.,

$$f$$<\/jats:tex-math>\n f<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is given the encoding

$$\\langle P \\rangle$$<\/jats:tex-math>\n \n \u27e8<\/mml:mo>\n P<\/mml:mi>\n \u27e9<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of a program

$$P$$<\/jats:tex-math>\n P<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and an input

$$x$$<\/jats:tex-math>\n x<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and computes

$$f(\\langle P \\rangle , x) = P(x)$$<\/jats:tex-math>\n \n f<\/mml:mi>\n (<\/mml:mo>\n \u27e8<\/mml:mo>\n P<\/mml:mi>\n \u27e9<\/mml:mo>\n ,<\/mml:mo>\n x<\/mml:mi>\n )<\/mml:mo>\n =<\/mml:mo>\n P<\/mml:mi>\n (<\/mml:mo>\n x<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. More concretely, we consider universal circuits, Turing machines, RAM machines, and branching programs, giving secure and conceptually simple card-based protocols in each case. We argue that card-based cryptography can be performed in a setting that is only very weakly interactive, which we call the \u201csurveillance\u201d model. Here, when Alice executes a protocol on the cards, the only task of Bob is to watch that Alice does not illegitimately turn over cards and that she shuffles in a way that nobody knows anything about the total permutation applied to the cards. We believe that because of this very limited interaction, our results can be called program obfuscation<\/jats:italic>. As a tool, we develop a useful sub-protocol

$${{\\mathrm{\\mathsf {sort}}}}_{\\varPi }{X} {\\uparrow } Y$$<\/jats:tex-math>\n \n \n sort<\/mml:mi>\n \u03a0<\/mml:mi>\n <\/mml:msub>\n X<\/mml:mi>\n \u2191<\/mml:mo>\n Y<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that couples the two equal-length sequences

$$X, Y$$<\/jats:tex-math>\n \n X<\/mml:mi>\n ,<\/mml:mo>\n Y<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and jointly and obliviously permutes them with the permutation

$$\\pi \\in \\varPi$$<\/jats:tex-math>\n \n \u03c0<\/mml:mi>\n \u2208<\/mml:mo>\n \u03a0<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that lexicographically minimizes

$${\\pi }(X)$$<\/jats:tex-math>\n \n \u03c0<\/mml:mi>\n (<\/mml:mo>\n X<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We argue that this generalizes ideas present in many existing card-based protocols. In fact, AND, XOR, bit copy [37], coupled rotation shuffles [30] and the \u201cpermutation division\u201d protocol of [22] can all be expressed as \u201ccoupled sort protocols\u201d.<\/jats:p>","DOI":"10.1007\/s00354-021-00149-9","type":"journal-article","created":{"date-parts":[[2022,2,12]],"date-time":"2022-02-12T09:02:43Z","timestamp":1644656563000},"page":"115-147","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Private Function Evaluation with Cards"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-3510-9669","authenticated-orcid":false,"given":"Alexander","family":"Koch","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-6477-0106","authenticated-orcid":false,"given":"Stefan","family":"Walzer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,12]]},"reference":[{"key":"149_CR1","unstructured":"Abbott, R.: Eleusis and Eleusis Express. http:\/\/www.logicmazes.com\/games\/eleusis\/ (visited on 10\/02\/2018)"},{"key":"149_CR2","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/978-3-319-67876-4_11","volume-title":"E-Business and Telecommunications","author":"D Achenbach","year":"2017","unstructured":"Achenbach, D., Borcherding, A., L\u00f6we, B., M\u00fcller-Quade, J., Rill, J.: Towards Realising Oblivious Voting. 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