# Analysis of NORX: Investigating Differential and Rotational Properties

Ontology type: schema:Chapter

### Chapter Info

DATE

2015-03-29

AUTHORS ABSTRACT

This paper presents a thorough analysis of the AEAD scheme NORX, focussing on differential and rotational properties. We first introduce mathematical models that describe differential propagation with respect to the non-linear operation of NORX. Afterwards, we adapt a framework previously proposed for ARX designs allowing us to automatise the search for differentials and characteristics. We give upper bounds on the differential probability for a small number of steps of the NORX core permutation. For example, in a scenario where an attacker can only modify the nonce during initialisation, we show that characteristics have probabilities of less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-60}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$32$$\end{document}-bit) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-53}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$64$$\end{document}-bit) after only one round. Furthermore, we describe how we found the best characteristics for four rounds, which have probabilities of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-584}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$32$$\end{document}-bit) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-836}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$64$$\end{document}-bit), respectively. Finally, we discuss some rotational properties of the core permutation which yield some first, rough bounds and can be used as a basis for future studies. More... »

PAGES

306-324

### Book

TITLE

Progress in Cryptology - LATINCRYPT 2014

ISBN

978-3-319-16294-2
978-3-319-16295-9

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-16295-9_17

DOI

http://dx.doi.org/10.1007/978-3-319-16295-9_17

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1016618707

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:

[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Applied Mathematics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Kudelski Security, Lausanne, Switzerland",
"id": "http://www.grid.ac/institutes/None",
"name": [
"Kudelski Security, Lausanne, Switzerland"
],
"type": "Organization"
},
"familyName": "Aumasson",
"givenName": "Jean-Philippe",
"id": "sg:person.012606440341.66",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012606440341.66"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Passau, Passau, Germany",
"id": "http://www.grid.ac/institutes/grid.11046.32",
"name": [
"University of Passau, Passau, Germany"
],
"type": "Organization"
},
"familyName": "Jovanovic",
"givenName": "Philipp",
"id": "sg:person.016300712435.04",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016300712435.04"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Coimbra, Coimbra, Portugal",
"id": "http://www.grid.ac/institutes/grid.8051.c",
"name": [
"University of Coimbra, Coimbra, Portugal"
],
"type": "Organization"
},
"familyName": "Neves",
"givenName": "Samuel",
"id": "sg:person.011136377232.42",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011136377232.42"
],
"type": "Person"
}
],
"datePublished": "2015-03-29",
"datePublishedReg": "2015-03-29",
"description": "This paper presents a thorough analysis of the AEAD scheme NORX, focussing on differential and rotational properties. We first introduce mathematical models that describe differential propagation with respect to the non-linear operation of NORX. Afterwards, we adapt a framework previously proposed for ARX designs allowing us to automatise the search for differentials and characteristics. We give upper bounds on the differential probability for a small number of steps of the NORX core permutation. For example, in a scenario where an attacker can only modify the nonce during initialisation, we show that characteristics have probabilities of less than \\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}$$2^{-60}$$\\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}$$32$$\\end{document}-bit) and \\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}$$2^{-53}$$\\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}$$64$$\\end{document}-bit) after only one round. Furthermore, we describe how we found the best characteristics for four rounds, which have probabilities of \\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}$$2^{-584}$$\\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}$$32$$\\end{document}-bit) and \\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}$$2^{-836}$$\\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}$$64$$\\end{document}-bit), respectively. Finally, we discuss some rotational properties of the core permutation which yield some first, rough bounds and can be used as a basis for future studies.",
"editor": [
{
"familyName": "Aranha",
"givenName": "Diego F.",
"type": "Person"
},
{
"familyName": "Menezes",
"givenName": "Alfred",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/978-3-319-16295-9_17",
"isAccessibleForFree": false,
"isPartOf": {
"isbn": [
"978-3-319-16294-2",
"978-3-319-16295-9"
],
"name": "Progress in Cryptology - LATINCRYPT 2014",
"type": "Book"
},
"keywords": [
"rotational properties",
"rough bounds",
"mathematical model",
"upper bounds",
"non-linear operations",
"core permutation",
"differential probability",
"bounds",
"ARX designs",
"probability",
"permutations",
"differential propagation",
"properties",
"thorough analysis",
"propagation",
"small number",
"initialisation",
"good characteristics",
"differential",
"model",
"framework",
"NORX",
"scenarios",
"number",
"respect",
"operation",
"characteristics",
"design",
"attacker",
"step",
"search",
"analysis",
"basis",
"nonce",
"rounds",
"study",
"future studies",
"example",
"paper"
],
"name": "Analysis of NORX: Investigating Differential and Rotational Properties",
"pagination": "306-324",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1016618707"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-3-319-16295-9_17"
]
}
],
"publisher": {
"name": "Springer Nature",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-3-319-16295-9_17",
"https://app.dimensions.ai/details/publication/pub.1016618707"
],
"sdDataset": "chapters",
"sdDatePublished": "2022-08-04T17:15",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220804/entities/gbq_results/chapter/chapter_16.jsonl",
"type": "Chapter",
"url": "https://doi.org/10.1007/978-3-319-16295-9_17"
}
]

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.10.1007/978-3-319-16295-9_17'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-16295-9_17'

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-16295-9_17'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-16295-9_17'

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

123 TRIPLES      22 PREDICATES      63 URIs      56 LITERALS      7 BLANK NODES

Subject Predicate Object
2 anzsrc-for:0102
3 schema:author N4c4c01f73df547ec806caaa600f45d35
4 schema:datePublished 2015-03-29
5 schema:datePublishedReg 2015-03-29
6 schema:description This paper presents a thorough analysis of the AEAD scheme NORX, focussing on differential and rotational properties. We first introduce mathematical models that describe differential propagation with respect to the non-linear operation of NORX. Afterwards, we adapt a framework previously proposed for ARX designs allowing us to automatise the search for differentials and characteristics. We give upper bounds on the differential probability for a small number of steps of the NORX core permutation. For example, in a scenario where an attacker can only modify the nonce during initialisation, we show that characteristics have probabilities of less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-60}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$32$$\end{document}-bit) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-53}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$64$$\end{document}-bit) after only one round. Furthermore, we describe how we found the best characteristics for four rounds, which have probabilities of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-584}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$32$$\end{document}-bit) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{-836}$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$64$$\end{document}-bit), respectively. Finally, we discuss some rotational properties of the core permutation which yield some first, rough bounds and can be used as a basis for future studies.
7 schema:editor N481244b4a3964b8f97b6558e48184c06
8 schema:genre chapter
9 schema:isAccessibleForFree false
10 schema:isPartOf N4b2f6b47d22741c488475f3b8b0a1f44
11 schema:keywords ARX designs
12 NORX
13 analysis
14 attacker
15 basis
16 bounds
17 characteristics
18 core permutation
19 design
20 differential
21 differential probability
22 differential propagation
23 example
24 framework
25 future studies
26 good characteristics
27 initialisation
28 mathematical model
29 model
30 non-linear operations
31 nonce
32 number
33 operation
34 paper
35 permutations
36 probability
37 propagation
38 properties
39 respect
40 rotational properties
41 rough bounds
42 rounds
43 scenarios
44 search
45 small number
46 step
47 study
48 thorough analysis
49 upper bounds
50 schema:name Analysis of NORX: Investigating Differential and Rotational Properties
51 schema:pagination 306-324
52 schema:productId Nba4f8f33d8904673b3618e3365f53222
53 Ne564409867334518bcd09654c4a2481f
55 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016618707
56 https://doi.org/10.1007/978-3-319-16295-9_17
57 schema:sdDatePublished 2022-08-04T17:15
59 schema:sdPublisher N138b0cf8c69140ae8d682a254310f95c
60 schema:url https://doi.org/10.1007/978-3-319-16295-9_17
62 sgo:sdDataset chapters
63 rdf:type schema:Chapter
64 N138b0cf8c69140ae8d682a254310f95c schema:name Springer Nature - SN SciGraph project
65 rdf:type schema:Organization
66 N15169e45e6df452e8de45c3f6b9b8092 rdf:first sg:person.016300712435.04
67 rdf:rest N7a9d742da7994af8833e0a55ed8154e8
68 N481244b4a3964b8f97b6558e48184c06 rdf:first N7dcec6e6faaf4cdf9d1df9476aafddf3
69 rdf:rest N7dd150c0b8fa4ec59537702b785e31ab
70 N4b2f6b47d22741c488475f3b8b0a1f44 schema:isbn 978-3-319-16294-2
71 978-3-319-16295-9
72 schema:name Progress in Cryptology - LATINCRYPT 2014
73 rdf:type schema:Book
74 N4c4c01f73df547ec806caaa600f45d35 rdf:first sg:person.012606440341.66
75 rdf:rest N15169e45e6df452e8de45c3f6b9b8092
76 N7a9d742da7994af8833e0a55ed8154e8 rdf:first sg:person.011136377232.42
77 rdf:rest rdf:nil
78 N7dcec6e6faaf4cdf9d1df9476aafddf3 schema:familyName Aranha
79 schema:givenName Diego F.
80 rdf:type schema:Person
82 rdf:rest rdf:nil
84 schema:givenName Alfred
85 rdf:type schema:Person
86 Nba4f8f33d8904673b3618e3365f53222 schema:name doi
87 schema:value 10.1007/978-3-319-16295-9_17
88 rdf:type schema:PropertyValue
90 rdf:type schema:Organisation
91 Ne564409867334518bcd09654c4a2481f schema:name dimensions_id
92 schema:value pub.1016618707
93 rdf:type schema:PropertyValue
94 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
95 schema:name Mathematical Sciences
96 rdf:type schema:DefinedTerm
97 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
98 schema:name Applied Mathematics
99 rdf:type schema:DefinedTerm
100 sg:person.011136377232.42 schema:affiliation grid-institutes:grid.8051.c
101 schema:familyName Neves
102 schema:givenName Samuel
103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011136377232.42
104 rdf:type schema:Person
105 sg:person.012606440341.66 schema:affiliation grid-institutes:None
106 schema:familyName Aumasson
107 schema:givenName Jean-Philippe
108 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012606440341.66
109 rdf:type schema:Person
110 sg:person.016300712435.04 schema:affiliation grid-institutes:grid.11046.32
111 schema:familyName Jovanovic
112 schema:givenName Philipp
113 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016300712435.04
114 rdf:type schema:Person
115 grid-institutes:None schema:alternateName Kudelski Security, Lausanne, Switzerland
116 schema:name Kudelski Security, Lausanne, Switzerland
117 rdf:type schema:Organization
118 grid-institutes:grid.11046.32 schema:alternateName University of Passau, Passau, Germany
119 schema:name University of Passau, Passau, Germany
120 rdf:type schema:Organization
121 grid-institutes:grid.8051.c schema:alternateName University of Coimbra, Coimbra, Portugal
122 schema:name University of Coimbra, Coimbra, Portugal
123 rdf:type schema:Organization