On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”

Standard

On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”. / Idrisova, Valeriya.

In: Cryptography and Communications, Vol. 11, No. 1, 01.01.2019, p. 21-39.

Research output: Contribution to journal › Article › peer-review

Harvard

Idrisova, V 2019, 'On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”', Cryptography and Communications, vol. 11, no. 1, pp. 21-39. https://doi.org/10.1007/s12095-018-0310-9

APA

Idrisova, V. (2019). On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”. Cryptography and Communications, 11(1), 21-39. https://doi.org/10.1007/s12095-018-0310-9

Vancouver

Idrisova V. On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”. Cryptography and Communications. 2019 Jan 1;11(1):21-39. doi: 10.1007/s12095-018-0310-9

Author

Idrisova, Valeriya. / On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”. In: Cryptography and Communications. 2019 ; Vol. 11, No. 1. pp. 21-39.

BibTeX

@article{cfa11ad2c49a4beaa47e89755ba76560,

title = "On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”",

abstract = "Almost perfect nonlinear (APN) functions are of great interest to many researchers since they have the optimal resistance to the differential attack. The existence of bijective APN functions in even number of variables is an important open problem, and there is only one known example of such a function at present. In this paper we consider a special subclass of 2-to-1 vectorial Boolean functions that can allow us to search and construct APN permutations. We proved that each 2-to-1 function is potentially EA-equivalent to a permutation and proposed an algorithm that generates special symbol sequences for constructing 2-to-1 APN functions. Also, we described two methods for searching APN permutations, that are based on sequences generated by this algorithm.",

keywords = "2-to-1 function, APN function, APN permutation, Boolean function, Differential uniformity, S-box",

author = "Valeriya Idrisova",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/s12095-018-0310-9",

language = "English",

volume = "11",

pages = "21--39",

journal = "Cryptography and Communications",

issn = "1936-2447",

publisher = "Springer Publishing Company",

number = "1",

}

RIS

TY - JOUR

T1 - On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem”

AU - Idrisova, Valeriya

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Almost perfect nonlinear (APN) functions are of great interest to many researchers since they have the optimal resistance to the differential attack. The existence of bijective APN functions in even number of variables is an important open problem, and there is only one known example of such a function at present. In this paper we consider a special subclass of 2-to-1 vectorial Boolean functions that can allow us to search and construct APN permutations. We proved that each 2-to-1 function is potentially EA-equivalent to a permutation and proposed an algorithm that generates special symbol sequences for constructing 2-to-1 APN functions. Also, we described two methods for searching APN permutations, that are based on sequences generated by this algorithm.

AB - Almost perfect nonlinear (APN) functions are of great interest to many researchers since they have the optimal resistance to the differential attack. The existence of bijective APN functions in even number of variables is an important open problem, and there is only one known example of such a function at present. In this paper we consider a special subclass of 2-to-1 vectorial Boolean functions that can allow us to search and construct APN permutations. We proved that each 2-to-1 function is potentially EA-equivalent to a permutation and proposed an algorithm that generates special symbol sequences for constructing 2-to-1 APN functions. Also, we described two methods for searching APN permutations, that are based on sequences generated by this algorithm.

KW - 2-to-1 function

KW - APN function

KW - APN permutation

KW - Boolean function

KW - Differential uniformity

KW - S-box

UR - http://www.scopus.com/inward/record.url?scp=85059692547&partnerID=8YFLogxK

U2 - 10.1007/s12095-018-0310-9

DO - 10.1007/s12095-018-0310-9

M3 - Article

AN - SCOPUS:85059692547

VL - 11

SP - 21

EP - 39

JO - Cryptography and Communications

JF - Cryptography and Communications

SN - 1936-2447

IS - 1

ER -

ID: 18070203