Secret Sharing Schemes for (k,n)-Consecutive Access Structures
We consider access structures over a set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {P}$$\end{document}...
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| creator | Herranz, Javier Sáez, Germán |
| description | We consider access structures over a set \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathcal {P}$$\end{document} of n participants, defined by a parameter k with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$1 \le k \le n$$\end{document} in the following way: a subset is authorized if it contains participants \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i,i+1,\ldots ,i+k-1$$\end{document}, for some \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i \in \{1,\ldots ,n-k+1\}$$\end{document}. We call such access structures, which may naturally appear in real applications involving distributed cryptography, (k, n)-consecutive.
We prove that these access structures are only ideal when \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=1,n-1,n$$\end{document}. Actually, we obtain the same result that has been obtained for other families of access structures: being ideal is equivalent to being a vector space access structure and is equivalent to having an optimal information rate strictly bigger than \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{2}{3}$$\end{document}. For the non-ideal cases, we give either the exact value of the optimal information rate, for \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{doc |
| doi_str_mv | 10.1007/978-3-030-00434-7_23 |
| format | Book Chapter |
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\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathcal {P}$$\end{document} of n participants, defined by a parameter k with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$1 \le k \le n$$\end{document} in the following way: a subset is authorized if it contains participants \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i,i+1,\ldots ,i+k-1$$\end{document}, for some \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i \in \{1,\ldots ,n-k+1\}$$\end{document}. We call such access structures, which may naturally appear in real applications involving distributed cryptography, (k, n)-consecutive.
We prove that these access structures are only ideal when \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=1,n-1,n$$\end{document}. Actually, we obtain the same result that has been obtained for other families of access structures: being ideal is equivalent to being a vector space access structure and is equivalent to having an optimal information rate strictly bigger than \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{2}{3}$$\end{document}. For the non-ideal cases, we give either the exact value of the optimal information rate, for \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=n-2$$\end{document} and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=n-3$$\end{document}, or some bounds on it.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783030004330</identifier><identifier>ISBN: 3030004333</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 3030004341</identifier><identifier>EISBN: 9783030004347</identifier><identifier>DOI: 10.1007/978-3-030-00434-7_23</identifier><identifier>OCLC: 1054246261</identifier><identifier>LCCallNum: QA268</identifier><language>eng</language><publisher>Switzerland: Springer International Publishing AG</publisher><subject>Criptografia ; Cryptography ; Ideal access structures ; Information rate ; Informàtica ; Matemàtica ; Secret sharing schemes ; Seguretat informàtica ; Àrees temàtiques de la UPC</subject><ispartof>Cryptology and Network Security, 2018, Vol.11124, p.463-480</ispartof><rights>Springer Nature Switzerland AG 2018</rights><rights>info:eu-repo/semantics/openAccess</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/6241663-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/978-3-030-00434-7_23$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/978-3-030-00434-7_23$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,775,776,780,789,881,26953,27904,38234,41421,42490</link.rule.ids></links><search><contributor>Papadimitratos, Panos</contributor><contributor>Camenisch, Jan</contributor><contributor>Papadimitratos, Panos</contributor><contributor>Camenisch, Jan</contributor><creatorcontrib>Herranz, Javier</creatorcontrib><creatorcontrib>Sáez, Germán</creatorcontrib><title>Secret Sharing Schemes for (k,n)-Consecutive Access Structures</title><title>Cryptology and Network Security</title><description>We consider access structures over a set \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathcal {P}$$\end{document} of n participants, defined by a parameter k with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$1 \le k \le n$$\end{document} in the following way: a subset is authorized if it contains participants \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i,i+1,\ldots ,i+k-1$$\end{document}, for some \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i \in \{1,\ldots ,n-k+1\}$$\end{document}. We call such access structures, which may naturally appear in real applications involving distributed cryptography, (k, n)-consecutive.
We prove that these access structures are only ideal when \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=1,n-1,n$$\end{document}. Actually, we obtain the same result that has been obtained for other families of access structures: being ideal is equivalent to being a vector space access structure and is equivalent to having an optimal information rate strictly bigger than \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{2}{3}$$\end{document}. For the non-ideal cases, we give either the exact value of the optimal information rate, for \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=n-2$$\end{document} and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=n-3$$\end{document}, or some bounds on it.</description><subject>Criptografia</subject><subject>Cryptography</subject><subject>Ideal access structures</subject><subject>Information rate</subject><subject>Informàtica</subject><subject>Matemàtica</subject><subject>Secret sharing schemes</subject><subject>Seguretat informàtica</subject><subject>Àrees temàtiques de la UPC</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783030004330</isbn><isbn>3030004333</isbn><isbn>3030004341</isbn><isbn>9783030004347</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2018</creationdate><recordtype>book_chapter</recordtype><sourceid>XX2</sourceid><recordid>eNpFkMlOwzAQQM0q2tI_4JAjSBg8tuM4F6SqYpMqcSicLceZ0NLSFNvh-3FaEAdrPMsbaR4hF8BugLHitiw0FZQJRhmTQtLCcHFAhiJVdgU4JANQAFQIWR6RcZr_6wl2TAbpz2lZSHFKhsByyaXiCs7IOISPNMWZLpXOB-Rujs5jzOYL65eb92zuFviJIWtan12urjdXdNpuArouLr8xmziHIWTz6DsXO4_hnJw0dh1w_BtH5O3h_nX6RGcvj8_TyYw6rvNIVV0AuMaiRQ1ga8dkXXPkVdPwJud5XdoSkLMGbVWBVEVVa4faamtB1emmEYH9Xhc6Zzw69M5G09rlf9I_zgpuRM5lDonheyZs-9PQm6ptV8EAM71ik5QZYZIoszNqesUJknto69uvDkM02FMON9HbtVvYbUQfjOISlBJGaG2kkuIHsq15wQ</recordid><startdate>2018</startdate><enddate>2018</enddate><creator>Herranz, Javier</creator><creator>Sáez, Germán</creator><general>Springer International Publishing AG</general><general>Springer International Publishing</general><general>Springer</general><scope>FFUUA</scope><scope>XX2</scope></search><sort><creationdate>2018</creationdate><title>Secret Sharing Schemes for (k,n)-Consecutive Access Structures</title><author>Herranz, Javier ; Sáez, Germán</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c285t-6d711cfaeae811adc04dd2e2bff2f525d9a91e20feabb1467bd8ce8a8aa16d043</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Criptografia</topic><topic>Cryptography</topic><topic>Ideal access structures</topic><topic>Information rate</topic><topic>Informàtica</topic><topic>Matemàtica</topic><topic>Secret sharing schemes</topic><topic>Seguretat informàtica</topic><topic>Àrees temàtiques de la UPC</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Herranz, Javier</creatorcontrib><creatorcontrib>Sáez, Germán</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Recercat</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Herranz, Javier</au><au>Sáez, Germán</au><au>Papadimitratos, Panos</au><au>Camenisch, Jan</au><au>Papadimitratos, Panos</au><au>Camenisch, Jan</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Secret Sharing Schemes for (k,n)-Consecutive Access Structures</atitle><btitle>Cryptology and Network Security</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2018</date><risdate>2018</risdate><volume>11124</volume><spage>463</spage><epage>480</epage><pages>463-480</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783030004330</isbn><isbn>3030004333</isbn><eisbn>3030004341</eisbn><eisbn>9783030004347</eisbn><abstract>We consider access structures over a set \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathcal {P}$$\end{document} of n participants, defined by a parameter k with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$1 \le k \le n$$\end{document} in the following way: a subset is authorized if it contains participants \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i,i+1,\ldots ,i+k-1$$\end{document}, for some \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$i \in \{1,\ldots ,n-k+1\}$$\end{document}. We call such access structures, which may naturally appear in real applications involving distributed cryptography, (k, n)-consecutive.
We prove that these access structures are only ideal when \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=1,n-1,n$$\end{document}. Actually, we obtain the same result that has been obtained for other families of access structures: being ideal is equivalent to being a vector space access structure and is equivalent to having an optimal information rate strictly bigger than \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{2}{3}$$\end{document}. For the non-ideal cases, we give either the exact value of the optimal information rate, for \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=n-2$$\end{document} and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$k=n-3$$\end{document}, or some bounds on it.</abstract><cop>Switzerland</cop><pub>Springer International Publishing AG</pub><doi>10.1007/978-3-030-00434-7_23</doi><oclcid>1054246261</oclcid><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Cryptology and Network Security, 2018, Vol.11124, p.463-480 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_csuc_recercat_oai_recercat_cat_2072_352451 |
| source | Springer Books; Recercat |
| subjects | Criptografia Cryptography Ideal access structures Information rate Informàtica Matemàtica Secret sharing schemes Seguretat informàtica Àrees temàtiques de la UPC |
| title | Secret Sharing Schemes for (k,n)-Consecutive Access Structures |
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