Beyond-Birthday-Bound Security for Tweakable Even-Mansour Ciphers with Linear Tweak and Key Mixing View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2015-12-30

AUTHORS

Benoît Cogliati , Yannick Seurin

ABSTRACT

The iterated Even-Mansour construction defines a block cipher from a tuple of public n-bit permutations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(P_1,\ldots ,P_r)$$\end{document} by alternatively xoring some n-bit round key \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_i$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i=0,\ldots ,r$$\end{document}, and applying permutation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_i$$\end{document} to the state. The tweakable Even-Mansour construction generalizes the conventional Even-Mansour construction by replacing the n-bit round keys by n-bit strings derived from a master key and a tweak, thereby defining a tweakable block cipher. Constructions of this type have been previously analyzed, but they were either secure only up to the birthday bound, or they used a nonlinear mixing function of the key and the tweak (typically, multiplication of the key and the tweak seen as elements of some finite field) which might be costly to implement. In this paper, we tackle the question of whether it is possible to achieve beyond-birthday-bound security for such a construction by using only linear operations for mixing the key and the tweak into the state. We answer positively, describing a 4-round construction with a 2n-bit master key and an n-bit tweak which is provably secure in the Random Permutation Model up to roughly \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{2n/3}$$\end{document} adversarial queries. More... »

PAGES

134-158

Book

TITLE

Advances in Cryptology – ASIACRYPT 2015

ISBN

978-3-662-48799-0
978-3-662-48800-3

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-662-48800-3_6

DOI

http://dx.doi.org/10.1007/978-3-662-48800-3_6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009957520


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0804", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Data Format", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Versailles, Versailles, France", 
          "id": "http://www.grid.ac/institutes/grid.12832.3a", 
          "name": [
            "University of Versailles, Versailles, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cogliati", 
        "givenName": "Beno\u00eet", 
        "id": "sg:person.010731237165.96", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010731237165.96"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "ANSSI, Paris, France", 
          "id": "http://www.grid.ac/institutes/None", 
          "name": [
            "ANSSI, Paris, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Seurin", 
        "givenName": "Yannick", 
        "id": "sg:person.011724731171.01", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011724731171.01"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2015-12-30", 
    "datePublishedReg": "2015-12-30", 
    "description": "The iterated Even-Mansour construction defines a block cipher from a tuple of public n-bit permutations \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(P_1,\\ldots ,P_r)$$\\end{document} by alternatively xoring some n-bit round key \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$k_i$$\\end{document}, \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$i=0,\\ldots ,r$$\\end{document}, and applying permutation \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P_i$$\\end{document} to the state. The tweakable Even-Mansour construction generalizes the conventional Even-Mansour construction by replacing the n-bit round keys by n-bit strings derived from a master key and a tweak, thereby defining a tweakable block cipher. Constructions of this type have been previously analyzed, but they were either secure only up\u00a0to the birthday bound, or they used a nonlinear mixing function of the key and the tweak (typically, multiplication of the key and the tweak seen as elements of some finite field) which might be costly to implement. In this paper, we tackle the question of whether it is possible to achieve beyond-birthday-bound security for such a construction by using only linear operations for mixing the key and the tweak into the state. We answer positively, describing a 4-round construction with a 2n-bit master key and an n-bit tweak which is provably secure in the Random Permutation Model up\u00a0to roughly \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2^{2n/3}$$\\end{document} adversarial queries.", 
    "editor": [
      {
        "familyName": "Iwata", 
        "givenName": "Tetsu", 
        "type": "Person"
      }, 
      {
        "familyName": "Cheon", 
        "givenName": "Jung Hee", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-662-48800-3_6", 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-3-662-48799-0", 
        "978-3-662-48800-3"
      ], 
      "name": "Advances in Cryptology \u2013 ASIACRYPT 2015", 
      "type": "Book"
    }, 
    "keywords": [
      "TWEAK", 
      "construction", 
      "types", 
      "birthday", 
      "function", 
      "birthday-bound security", 
      "key", 
      "state", 
      "master key", 
      "paper", 
      "questions", 
      "security", 
      "operation", 
      "permutation model", 
      "model", 
      "cipher", 
      "tuples", 
      "permutations", 
      "round keys", 
      "string", 
      "tweakable block cipher", 
      "queries", 
      "mixing", 
      "Even-Mansour construction", 
      "block cipher", 
      "n-bit permutations", 
      "Mansour construction", 
      "n-bit strings", 
      "linear operation", 
      "random permutation model", 
      "adversarial queries", 
      "Tweakable", 
      "Mansour ciphers"
    ], 
    "name": "Beyond-Birthday-Bound Security for Tweakable Even-Mansour Ciphers with Linear Tweak and Key Mixing", 
    "pagination": "134-158", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1009957520"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-662-48800-3_6"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-662-48800-3_6", 
      "https://app.dimensions.ai/details/publication/pub.1009957520"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-11-24T21:19", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221124/entities/gbq_results/chapter/chapter_467.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-662-48800-3_6"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-48800-3_6'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-48800-3_6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-48800-3_6'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-48800-3_6'


 

This table displays all metadata directly associated to this object as RDF triples.

107 TRIPLES      22 PREDICATES      57 URIs      50 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-662-48800-3_6 schema:about anzsrc-for:08
2 anzsrc-for:0804
3 schema:author Nd97b70072b4b48e3a191fa27e370574f
4 schema:datePublished 2015-12-30
5 schema:datePublishedReg 2015-12-30
6 schema:description The iterated Even-Mansour construction defines a block cipher from a tuple of public n-bit permutations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(P_1,\ldots ,P_r)$$\end{document} by alternatively xoring some n-bit round key \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_i$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i=0,\ldots ,r$$\end{document}, and applying permutation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_i$$\end{document} to the state. The tweakable Even-Mansour construction generalizes the conventional Even-Mansour construction by replacing the n-bit round keys by n-bit strings derived from a master key and a tweak, thereby defining a tweakable block cipher. Constructions of this type have been previously analyzed, but they were either secure only up to the birthday bound, or they used a nonlinear mixing function of the key and the tweak (typically, multiplication of the key and the tweak seen as elements of some finite field) which might be costly to implement. In this paper, we tackle the question of whether it is possible to achieve beyond-birthday-bound security for such a construction by using only linear operations for mixing the key and the tweak into the state. We answer positively, describing a 4-round construction with a 2n-bit master key and an n-bit tweak which is provably secure in the Random Permutation Model up to roughly \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{2n/3}$$\end{document} adversarial queries.
7 schema:editor N9e21697647ab40f68f23048b18502bdc
8 schema:genre chapter
9 schema:isAccessibleForFree true
10 schema:isPartOf N10d8f098145847689f06dabe2e353425
11 schema:keywords Even-Mansour construction
12 Mansour ciphers
13 Mansour construction
14 TWEAK
15 Tweakable
16 adversarial queries
17 birthday
18 birthday-bound security
19 block cipher
20 cipher
21 construction
22 function
23 key
24 linear operation
25 master key
26 mixing
27 model
28 n-bit permutations
29 n-bit strings
30 operation
31 paper
32 permutation model
33 permutations
34 queries
35 questions
36 random permutation model
37 round keys
38 security
39 state
40 string
41 tuples
42 tweakable block cipher
43 types
44 schema:name Beyond-Birthday-Bound Security for Tweakable Even-Mansour Ciphers with Linear Tweak and Key Mixing
45 schema:pagination 134-158
46 schema:productId N3ea9469d131b4e1293222988f931cca1
47 N896e6b2932c24b4a83871285bc5cda88
48 schema:publisher Nce922933f52e47c09971ec8173cf65e9
49 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009957520
50 https://doi.org/10.1007/978-3-662-48800-3_6
51 schema:sdDatePublished 2022-11-24T21:19
52 schema:sdLicense https://scigraph.springernature.com/explorer/license/
53 schema:sdPublisher N7d5e90a2b82240659c3ca5ff2fc4d989
54 schema:url https://doi.org/10.1007/978-3-662-48800-3_6
55 sgo:license sg:explorer/license/
56 sgo:sdDataset chapters
57 rdf:type schema:Chapter
58 N067f03da28de4514a3c99adf62ed0511 schema:familyName Iwata
59 schema:givenName Tetsu
60 rdf:type schema:Person
61 N10d8f098145847689f06dabe2e353425 schema:isbn 978-3-662-48799-0
62 978-3-662-48800-3
63 schema:name Advances in Cryptology – ASIACRYPT 2015
64 rdf:type schema:Book
65 N3ea9469d131b4e1293222988f931cca1 schema:name dimensions_id
66 schema:value pub.1009957520
67 rdf:type schema:PropertyValue
68 N4371ba92ef8b4886bcff21647604e6fe rdf:first sg:person.011724731171.01
69 rdf:rest rdf:nil
70 N4e7983ace7b742bc9523a1e591a61ce4 schema:familyName Cheon
71 schema:givenName Jung Hee
72 rdf:type schema:Person
73 N7d5e90a2b82240659c3ca5ff2fc4d989 schema:name Springer Nature - SN SciGraph project
74 rdf:type schema:Organization
75 N896e6b2932c24b4a83871285bc5cda88 schema:name doi
76 schema:value 10.1007/978-3-662-48800-3_6
77 rdf:type schema:PropertyValue
78 N9e21697647ab40f68f23048b18502bdc rdf:first N067f03da28de4514a3c99adf62ed0511
79 rdf:rest Na4f50a20253e43e8b49173c44161ff6c
80 Na4f50a20253e43e8b49173c44161ff6c rdf:first N4e7983ace7b742bc9523a1e591a61ce4
81 rdf:rest rdf:nil
82 Nce922933f52e47c09971ec8173cf65e9 schema:name Springer Nature
83 rdf:type schema:Organisation
84 Nd97b70072b4b48e3a191fa27e370574f rdf:first sg:person.010731237165.96
85 rdf:rest N4371ba92ef8b4886bcff21647604e6fe
86 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
87 schema:name Information and Computing Sciences
88 rdf:type schema:DefinedTerm
89 anzsrc-for:0804 schema:inDefinedTermSet anzsrc-for:
90 schema:name Data Format
91 rdf:type schema:DefinedTerm
92 sg:person.010731237165.96 schema:affiliation grid-institutes:grid.12832.3a
93 schema:familyName Cogliati
94 schema:givenName Benoît
95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010731237165.96
96 rdf:type schema:Person
97 sg:person.011724731171.01 schema:affiliation grid-institutes:None
98 schema:familyName Seurin
99 schema:givenName Yannick
100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011724731171.01
101 rdf:type schema:Person
102 grid-institutes:None schema:alternateName ANSSI, Paris, France
103 schema:name ANSSI, Paris, France
104 rdf:type schema:Organization
105 grid-institutes:grid.12832.3a schema:alternateName University of Versailles, Versailles, France
106 schema:name University of Versailles, Versailles, France
107 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...