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Nonmalleable encryption of quantum information
We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension d ): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a sch...
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| Published in: | Journal of mathematical physics 2009-04, Vol.50 (4), p.042106-042106-8 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c512t-648abe80ed7bdc7373107bec58fae1dc3bfe9dd2991acd8ffaa0a321b16c71da3 |
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| cites | cdi_FETCH-LOGICAL-c512t-648abe80ed7bdc7373107bec58fae1dc3bfe9dd2991acd8ffaa0a321b16c71da3 |
| container_end_page | 042106-8 |
| container_issue | 4 |
| container_start_page | 042106 |
| container_title | Journal of mathematical physics |
| container_volume | 50 |
| creator | Ambainis, Andris Bouda, Jan Winter, Andreas |
| description | We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension
d
): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a unitary 2-design [Dankert,
et al.
, e-print arXiv:quant-ph/0606161
], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of
(
d
2
−
1
)
2
+
1
on the number of unitaries in a 2-design [Gross,
et al.
, J. Math. Phys.
48, 052104 (2007)], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with
≤
d
5
elements, we show that there are always approximate 2-designs with
O
(
ϵ
−
2
d
4
log
d
)
elements. |
| doi_str_mv | 10.1063/1.3094756 |
| format | article |
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d
): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a unitary 2-design [Dankert,
et al.
, e-print arXiv:quant-ph/0606161
], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of
(
d
2
−
1
)
2
+
1
on the number of unitaries in a 2-design [Gross,
et al.
, J. Math. Phys.
48, 052104 (2007)], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with
≤
d
5
elements, we show that there are always approximate 2-designs with
O
(
ϵ
−
2
d
4
log
d
)
elements.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.3094756</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>Approximation ; Data encryption ; Exact sciences and technology ; Information ; Mathematical methods in physics ; Mathematics ; Physics ; Quantum physics ; Sciences and techniques of general use</subject><ispartof>Journal of mathematical physics, 2009-04, Vol.50 (4), p.042106-042106-8</ispartof><rights>American Institute of Physics</rights><rights>2009 American Institute of Physics</rights><rights>2009 INIST-CNRS</rights><rights>Copyright American Institute of Physics Apr 2009</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c512t-648abe80ed7bdc7373107bec58fae1dc3bfe9dd2991acd8ffaa0a321b16c71da3</citedby><cites>FETCH-LOGICAL-c512t-648abe80ed7bdc7373107bec58fae1dc3bfe9dd2991acd8ffaa0a321b16c71da3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.3094756$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,782,784,795,27924,27925,76383</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21452195$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Ambainis, Andris</creatorcontrib><creatorcontrib>Bouda, Jan</creatorcontrib><creatorcontrib>Winter, Andreas</creatorcontrib><title>Nonmalleable encryption of quantum information</title><title>Journal of mathematical physics</title><description>We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension
d
): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a unitary 2-design [Dankert,
et al.
, e-print arXiv:quant-ph/0606161
], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of
(
d
2
−
1
)
2
+
1
on the number of unitaries in a 2-design [Gross,
et al.
, J. Math. Phys.
48, 052104 (2007)], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with
≤
d
5
elements, we show that there are always approximate 2-designs with
O
(
ϵ
−
2
d
4
log
d
)
elements.</description><subject>Approximation</subject><subject>Data encryption</subject><subject>Exact sciences and technology</subject><subject>Information</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>Physics</subject><subject>Quantum physics</subject><subject>Sciences and techniques of general use</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsFYP_oMgeFBI3dnNx-YiSPELil70vEz2A1KSbLubCP33pjaoIPU0MDzvM8xLyDnQGdCM38CM0yLJ0-yATICKIs6zVBySCaWMxSwR4pichLCkFEAkyYTMXlzbYF0bLGsTmVb5zaqrXBs5G617bLu-iarWOt_gdn1KjizWwZyNc0reH-7f5k_x4vXxeX63iFUKrIuzRGBpBDU6L7XKec6B5qVRqbBoQCteWlNozYoCUGlhLSJFzqCETOWgkU_Jxc678m7dm9DJpet9O5yUDNIMMs7SAbraQcq7ELyxcuWrBv1GApXbNiTIsY2BvRyFGBTW1mOrqvAdYJCkDIqt83bHBVV1Xy_vl_6uTo7VDYLrfYIP53_CcqXtf_DfFz4BxCKQ1g</recordid><startdate>20090401</startdate><enddate>20090401</enddate><creator>Ambainis, Andris</creator><creator>Bouda, Jan</creator><creator>Winter, Andreas</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope></search><sort><creationdate>20090401</creationdate><title>Nonmalleable encryption of quantum information</title><author>Ambainis, Andris ; Bouda, Jan ; Winter, Andreas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c512t-648abe80ed7bdc7373107bec58fae1dc3bfe9dd2991acd8ffaa0a321b16c71da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Approximation</topic><topic>Data encryption</topic><topic>Exact sciences and technology</topic><topic>Information</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>Physics</topic><topic>Quantum physics</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ambainis, Andris</creatorcontrib><creatorcontrib>Bouda, Jan</creatorcontrib><creatorcontrib>Winter, Andreas</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ambainis, Andris</au><au>Bouda, Jan</au><au>Winter, Andreas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonmalleable encryption of quantum information</atitle><jtitle>Journal of mathematical physics</jtitle><date>2009-04-01</date><risdate>2009</risdate><volume>50</volume><issue>4</issue><spage>042106</spage><epage>042106-8</epage><pages>042106-042106-8</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension
d
): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a unitary 2-design [Dankert,
et al.
, e-print arXiv:quant-ph/0606161
], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of
(
d
2
−
1
)
2
+
1
on the number of unitaries in a 2-design [Gross,
et al.
, J. Math. Phys.
48, 052104 (2007)], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with
≤
d
5
elements, we show that there are always approximate 2-designs with
O
(
ϵ
−
2
d
4
log
d
)
elements.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.3094756</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2009-04, Vol.50 (4), p.042106-042106-8 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_crossref_primary_10_1063_1_3094756 |
| source | American Institute of Physics (AIP) Publications; American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list) |
| subjects | Approximation Data encryption Exact sciences and technology Information Mathematical methods in physics Mathematics Physics Quantum physics Sciences and techniques of general use |
| title | Nonmalleable encryption of quantum information |
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