A note of perfect nonlinear functions

Xiyong Zhang; Hua Guo; Jinjiang Yuan

doi:10.1007/11935070_18

A note of perfect nonlinear functions

Xiyong Zhang
, Hua Guo
, Jinjiang Yuan

School of Cyber Science and Technology

Zhengzhou University
Information Engineering University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

Perfect nonlinear functions are of importance in cryptography. By using Galois rings and investigating the character values of corresponding relative difference sets, we construct a perfect nonlinear function from ℤⁿp² to Zℤ^mp²where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from Z²2p to Z_2p if and only if p = 2, and that there doesn't exist a perfect nonlinear function from Z²ⁿ₂^klto Z^m2^k if m > n and l(l is odd) is self-conjugate modulo 2^k(k ≥ 1).

Original language	English
Title of host publication	Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings
Publisher	Springer Verlag
Pages	259-269
Number of pages	11
ISBN (Print)	9783540494621
DOIs	https://doi.org/10.1007/11935070_18
State	Published - 2006
Event	5th International Conference on Cryptology and Network Security, CANS 2006 - Suzhou, China Duration: 8 Dec 2006 → 10 Dec 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4301 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Conference on Cryptology and Network Security, CANS 2006
Country/Territory	China
City	Suzhou
Period	8/12/06 → 10/12/06

Access to Document

10.1007/11935070_18

Cite this

Zhang, X., Guo, H., & Yuan, J. (2006). A note of perfect nonlinear functions. In Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings (pp. 259-269). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4301 LNCS). Springer Verlag. https://doi.org/10.1007/11935070_18

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title = "A note of perfect nonlinear functions",

abstract = "Perfect nonlinear functions are of importance in cryptography. By using Galois rings and investigating the character values of corresponding relative difference sets, we construct a perfect nonlinear function from ℤnp2 to Zℤmp2where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from Z22p to Z2p if and only if p = 2, and that there doesn't exist a perfect nonlinear function from Z2n2klto Zm2k if m > n and l(l is odd) is self-conjugate modulo 2k(k ≥ 1).",

author = "Xiyong Zhang and Hua Guo and Jinjiang Yuan",

year = "2006",

doi = "10.1007/11935070\_18",

language = "英语",

isbn = "9783540494621",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "259--269",

booktitle = "Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings",

address = "德国",

note = "5th International Conference on Cryptology and Network Security, CANS 2006 ; Conference date: 08-12-2006 Through 10-12-2006",

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Zhang, X, Guo, H & Yuan, J 2006, A note of perfect nonlinear functions. in Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4301 LNCS, Springer Verlag, pp. 259-269, 5th International Conference on Cryptology and Network Security, CANS 2006, Suzhou, China, 8/12/06. https://doi.org/10.1007/11935070_18

A note of perfect nonlinear functions. / Zhang, Xiyong; Guo, Hua; Yuan, Jinjiang.
Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings. Springer Verlag, 2006. p. 259-269 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4301 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Perfect nonlinear functions are of importance in cryptography. By using Galois rings and investigating the character values of corresponding relative difference sets, we construct a perfect nonlinear function from ℤnp2 to Zℤmp2where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from Z22p to Z2p if and only if p = 2, and that there doesn't exist a perfect nonlinear function from Z2n2klto Zm2k if m > n and l(l is odd) is self-conjugate modulo 2k(k ≥ 1).

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BT - Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings

PB - Springer Verlag

T2 - 5th International Conference on Cryptology and Network Security, CANS 2006

Y2 - 8 December 2006 through 10 December 2006

ER -

A note of perfect nonlinear functions

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