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

网络空间安全学院

Zhengzhou University
Information Engineering University

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

3 引用（Scopus）

摘要

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).

源语言	英语
主期刊名	Cryptology and Network Security - 5th International Conference, CANS 2006, Proceedings
出版商	Springer Verlag
页	259-269
页数	11
ISBN（印刷版）	9783540494621
DOI	https://doi.org/10.1007/11935070_18
出版状态	已出版 - 2006
活动	5th International Conference on Cryptology and Network Security, CANS 2006 - Suzhou, 中国期限: 8 12月 2006 → 10 12月 2006

出版系列

姓名	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
卷	4301 LNCS
ISSN（印刷版）	0302-9743
ISSN（电子版）	1611-3349

会议

会议	5th International Conference on Cryptology and Network Security, CANS 2006
国家/地区	中国
市	Suzhou
时期	8/12/06 → 10/12/06

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10.1007/11935070_18

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引用此

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

@inproceedings{7576d26d0089417392df8f1a4668c611,

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",

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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. 在 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), 卷 4301 LNCS, Springer Verlag, 页码 259-269, 5th International Conference on Cryptology and Network Security, CANS 2006, Suzhou, 中国, 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. 页码 259-269 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 卷 4301 LNCS).

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

TY - GEN

T1 - A note of perfect nonlinear functions

AU - Zhang, Xiyong

AU - Guo, Hua

AU - Yuan, Jinjiang

PY - 2006

Y1 - 2006

N2 - 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).

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).

UR - https://www.scopus.com/pages/publications/84885926084

U2 - 10.1007/11935070_18

DO - 10.1007/11935070_18

M3 - 会议稿件

AN - SCOPUS:84885926084

SN - 9783540494621

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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EP - 269

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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