Factorizations in the elementary Abelian p-group and their cryptographic significance View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1994-12

AUTHORS

Minghua Qu, S. A. Vanstone

ABSTRACT

Let G be a finite group and let Ai 1 ≤ i ≤ s, be subsets of G where ¦Ai¦ ≥ 2, 1 ≤ i ≤ s and s ≥ 2. We say that (A1, A2,..., A3) is a factorization of G if and only if for each g ε G there is exactly one way to express g = a1a1a2··· a3, where aj ε Ai, 1 ≤ i ≤ s.The problem of finding factorizations of this type was first introduced by Hajos [3] in 1941. Since then a number of papers have appeared on the subject. More recently, Magliveras [6] has applied factorization of permutation groups to cryptography to obtain a private-key cryptosystem. Factorizations in the elementary abelian p-group were exploited (but not explicitly stated in these terms) by Webb [13] to produce a public-key cryptosystem conceptually similar to cryptosystems based on the knapsack problem.Using the result that certain types of factorizations in the elementary abelian p-group are necessarily transversal (a term introduced by Magliveras), this paper shows that the public-key system proposed by Webb is insecure. More... »

PAGES

201-212

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00203963

DOI

http://dx.doi.org/10.1007/bf00203963

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1045581594


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": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.46078.3d", 
          "name": [
            "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Qu", 
        "givenName": "Minghua", 
        "id": "sg:person.010300257167.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010300257167.71"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.46078.3d", 
          "name": [
            "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Vanstone", 
        "givenName": "S. A.", 
        "id": "sg:person.010344544767.07", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02451113", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053438151", 
          "https://doi.org/10.1007/bf02451113"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02404700", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023165869", 
          "https://doi.org/10.1007/bf02404700"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02025232", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031909942", 
          "https://doi.org/10.1007/bf02025232"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01904843", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002592021", 
          "https://doi.org/10.1007/bf01904843"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01180974", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011800905", 
          "https://doi.org/10.1007/bf01180974"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02021311", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006500342", 
          "https://doi.org/10.1007/bf02021311"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1994-12", 
    "datePublishedReg": "1994-12-01", 
    "description": "Let G be a finite group and let Ai 1 \u2264 i \u2264 s, be subsets of G where \u00a6Ai\u00a6 \u2265 2, 1 \u2264 i \u2264 s and s \u2265 2. We say that (A1, A2,..., A3) is a factorization of G if and only if for each g \u03b5 G there is exactly one way to express g = a1a1a2\u00b7\u00b7\u00b7 a3, where aj \u03b5 Ai, 1 \u2264 i \u2264 s.The problem of finding factorizations of this type was first introduced by Hajos [3] in 1941. Since then a number of papers have appeared on the subject. More recently, Magliveras [6] has applied factorization of permutation groups to cryptography to obtain a private-key cryptosystem. Factorizations in the elementary abelian p-group were exploited (but not explicitly stated in these terms) by Webb [13] to produce a public-key cryptosystem conceptually similar to cryptosystems based on the knapsack problem.Using the result that certain types of factorizations in the elementary abelian p-group are necessarily transversal (a term introduced by Magliveras), this paper shows that the public-key system proposed by Webb is insecure.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf00203963", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136278", 
        "issn": [
          "0933-2790", 
          "1432-1378"
        ], 
        "name": "Journal of Cryptology", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "7"
      }
    ], 
    "keywords": [
      "private-key cryptosystem", 
      "public key cryptosystem", 
      "public key system", 
      "knapsack problem", 
      "cryptosystem", 
      "cryptographic significance", 
      "AI", 
      "factorization", 
      "cryptography", 
      "number of papers", 
      "system", 
      "certain types", 
      "way", 
      "subset", 
      "permutation groups", 
      "number", 
      "Magliveras", 
      "types", 
      "results", 
      "elementary abelian p-group", 
      "AI-1", 
      "subjects", 
      "significance", 
      "group", 
      "finite group", 
      "abelian p-group", 
      "Webb", 
      "P group", 
      "A3", 
      "problem", 
      "paper", 
      "Hajos"
    ], 
    "name": "Factorizations in the elementary Abelian p-group and their cryptographic significance", 
    "pagination": "201-212", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1045581594"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf00203963"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf00203963", 
      "https://app.dimensions.ai/details/publication/pub.1045581594"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-09-02T15:47", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_228.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf00203963"
  }
]
 

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/bf00203963'

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/bf00203963'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00203963'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00203963'


 

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

120 TRIPLES      21 PREDICATES      63 URIs      49 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf00203963 schema:about anzsrc-for:08
2 anzsrc-for:0804
3 schema:author N44e6d9b9ccc94736a18b0caf40f07137
4 schema:citation sg:pub.10.1007/bf01180974
5 sg:pub.10.1007/bf01904843
6 sg:pub.10.1007/bf02021311
7 sg:pub.10.1007/bf02025232
8 sg:pub.10.1007/bf02404700
9 sg:pub.10.1007/bf02451113
10 schema:datePublished 1994-12
11 schema:datePublishedReg 1994-12-01
12 schema:description Let G be a finite group and let Ai 1 ≤ i ≤ s, be subsets of G where ¦Ai¦ ≥ 2, 1 ≤ i ≤ s and s ≥ 2. We say that (A1, A2,..., A3) is a factorization of G if and only if for each g ε G there is exactly one way to express g = a1a1a2··· a3, where aj ε Ai, 1 ≤ i ≤ s.The problem of finding factorizations of this type was first introduced by Hajos [3] in 1941. Since then a number of papers have appeared on the subject. More recently, Magliveras [6] has applied factorization of permutation groups to cryptography to obtain a private-key cryptosystem. Factorizations in the elementary abelian p-group were exploited (but not explicitly stated in these terms) by Webb [13] to produce a public-key cryptosystem conceptually similar to cryptosystems based on the knapsack problem.Using the result that certain types of factorizations in the elementary abelian p-group are necessarily transversal (a term introduced by Magliveras), this paper shows that the public-key system proposed by Webb is insecure.
13 schema:genre article
14 schema:isAccessibleForFree false
15 schema:isPartOf Nb9d3fba78e42458e92000b4b37315901
16 Nc16be9f9891d462f8b59f8a9764ae359
17 sg:journal.1136278
18 schema:keywords A3
19 AI
20 AI-1
21 Hajos
22 Magliveras
23 P group
24 Webb
25 abelian p-group
26 certain types
27 cryptographic significance
28 cryptography
29 cryptosystem
30 elementary abelian p-group
31 factorization
32 finite group
33 group
34 knapsack problem
35 number
36 number of papers
37 paper
38 permutation groups
39 private-key cryptosystem
40 problem
41 public key cryptosystem
42 public key system
43 results
44 significance
45 subjects
46 subset
47 system
48 types
49 way
50 schema:name Factorizations in the elementary Abelian p-group and their cryptographic significance
51 schema:pagination 201-212
52 schema:productId N37d1ac100619448e9299d234d77eccf1
53 Nddef3bb8d77f4021ad6ee7eb0ad2cfc2
54 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045581594
55 https://doi.org/10.1007/bf00203963
56 schema:sdDatePublished 2022-09-02T15:47
57 schema:sdLicense https://scigraph.springernature.com/explorer/license/
58 schema:sdPublisher N5bda40ceb56844cfb86699a63041c482
59 schema:url https://doi.org/10.1007/bf00203963
60 sgo:license sg:explorer/license/
61 sgo:sdDataset articles
62 rdf:type schema:ScholarlyArticle
63 N37d1ac100619448e9299d234d77eccf1 schema:name dimensions_id
64 schema:value pub.1045581594
65 rdf:type schema:PropertyValue
66 N44e6d9b9ccc94736a18b0caf40f07137 rdf:first sg:person.010300257167.71
67 rdf:rest N97d8238d993d4f13b44061278471c7f1
68 N5bda40ceb56844cfb86699a63041c482 schema:name Springer Nature - SN SciGraph project
69 rdf:type schema:Organization
70 N97d8238d993d4f13b44061278471c7f1 rdf:first sg:person.010344544767.07
71 rdf:rest rdf:nil
72 Nb9d3fba78e42458e92000b4b37315901 schema:issueNumber 4
73 rdf:type schema:PublicationIssue
74 Nc16be9f9891d462f8b59f8a9764ae359 schema:volumeNumber 7
75 rdf:type schema:PublicationVolume
76 Nddef3bb8d77f4021ad6ee7eb0ad2cfc2 schema:name doi
77 schema:value 10.1007/bf00203963
78 rdf:type schema:PropertyValue
79 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
80 schema:name Information and Computing Sciences
81 rdf:type schema:DefinedTerm
82 anzsrc-for:0804 schema:inDefinedTermSet anzsrc-for:
83 schema:name Data Format
84 rdf:type schema:DefinedTerm
85 sg:journal.1136278 schema:issn 0933-2790
86 1432-1378
87 schema:name Journal of Cryptology
88 schema:publisher Springer Nature
89 rdf:type schema:Periodical
90 sg:person.010300257167.71 schema:affiliation grid-institutes:grid.46078.3d
91 schema:familyName Qu
92 schema:givenName Minghua
93 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010300257167.71
94 rdf:type schema:Person
95 sg:person.010344544767.07 schema:affiliation grid-institutes:grid.46078.3d
96 schema:familyName Vanstone
97 schema:givenName S. A.
98 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07
99 rdf:type schema:Person
100 sg:pub.10.1007/bf01180974 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011800905
101 https://doi.org/10.1007/bf01180974
102 rdf:type schema:CreativeWork
103 sg:pub.10.1007/bf01904843 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002592021
104 https://doi.org/10.1007/bf01904843
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/bf02021311 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006500342
107 https://doi.org/10.1007/bf02021311
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/bf02025232 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031909942
110 https://doi.org/10.1007/bf02025232
111 rdf:type schema:CreativeWork
112 sg:pub.10.1007/bf02404700 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023165869
113 https://doi.org/10.1007/bf02404700
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/bf02451113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053438151
116 https://doi.org/10.1007/bf02451113
117 rdf:type schema:CreativeWork
118 grid-institutes:grid.46078.3d schema:alternateName Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
119 schema:name Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
120 rdf:type schema:Organization
 




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


...