高效构造基于有限域上莫德尔椭圆曲线的密码置换盒

Naveed Ahmed AZAM; Umar HAYAT; Ikram ULLAH

doi:10.1631/FITEE.1800434

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高效构造基于有限域上莫德尔椭圆曲线的密码置换盒

常规文章 | Updated：2022-05-19

- 高效构造基于有限域上莫德尔椭圆曲线的密码置换盒
- Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field
- 信息与电子工程前沿（英文） 2019年20卷第10期页码：1378-1389
- Affiliations：
  
  Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
  Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
- Author bio：
  
  Naveed Ahmed AZAM, E-mail: azam@amp.i.kyoto-u.ac.jp
  [ "Umar HAYAT, E-mail: umar.hayat@qau.edu.pk" ]
- Funds：
  
  Project supported by the JSPS KAKENHI (No. 18J23484)
- DOI：10.1631/FITEE.1800434
  中图分类号： TP309
- 收稿：2018-07-18，
  
  修回：2019-10-10，
  
  纸质出版：2019-10
- Accepted：
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Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH. 高效构造基于有限域上莫德尔椭圆曲线的密码置换盒[J]. 信息与电子工程前沿（英文）, 2019,20(10):1378-1389.

Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH. Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1378-1389.
Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH. 高效构造基于有限域上莫德尔椭圆曲线的密码置换盒[J]. 信息与电子工程前沿（英文）, 2019,20(10):1378-1389. DOI： 10.1631/FITEE.1800434.

Naveed Ahmed AZAM, Umar HAYAT, Ikram ULLAH. Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1378-1389. DOI： 10.1631/FITEE.1800434.

摘要

椭圆曲线密码体制与其他密码体制相比有密钥小、安全性高等优点，被广泛应用于各种安全系统。在许多著名安全系统中，仅置换盒是非线性结构。最近研究表明，用动态置换盒代替静态置换盒可提高密码系统安全性，因此需构造新的安全置换盒。提出一种高效构造置换盒方法，该方法基于素数域上的一类莫德尔椭圆曲线，并通过定义不同总阶数实现。对于每个输入，该方法在线性时间与恒定空间内输出一个置换盒。因此，与现有基于椭圆曲线的置换盒生成方法相比，所提方法占用更少时间和空间。计算结果表明，所提方法能生成加密性强的置换盒，且其安全性与现有基于其他数学结构的置换盒相当。

Abstract

Elliptic curve cryptography has been used in many security systems due to its small key size and high security compared with other cryptosystems. In many well-known security systems

a substitution box (S-box) is the only non-linear component. Recently

it has been shown that the security of a cryptosystem can be improved using dynamic S-boxes instead of a static S-box. This necessitates the construction of new secure S-boxes. We propose an efficient method to generate S-boxes that are based on a class of Mordell elliptic curves over prime fields and achieved by defining different total orders. The proposed scheme is developed in such a way that for each input it outputs an S-box in linear time and constant space. Due to this property

our method takes less time and space than the existing S-box construction methods over elliptic curves. Computational results show that the proposed method is capable of generating cryptographically strong S-boxes with security comparable to some of the existing S-boxes constructed via different mathematical structures.

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references

P Agarwal , , , A Singh , , , A Kilicman . . Development of key- dependent dynamic S-boxes with dynamic irreducible polynomial and affine constant . . Adv Mech Eng , , 2018 . . 10 ( ( 7 ): ): 1 - - 18 . . DOI: 10.1177/1687814018781638 http://doi.org/10.1177/1687814018781638 . .

NA Azam . . A novel fuzzy encryption technique based on multiple right translated AES gray S-boxes and phase embedding . . Secur Commun Netw , , 2017 . . 2017 1 - - 9 . . DOI: 10.1155/2017/5790189 http://doi.org/10.1155/2017/5790189 . .

G Chen . . A novel heuristic method for obtaining S-boxes . . Chaos Sol Fract , , 2008 . . 36 ( ( 4 ): ): 1028 - - 1036 . . DOI: 10.1016/j.chaos.2006.08.003 http://doi.org/10.1016/j.chaos.2006.08.003 . .

G Chen , , , Y Chen , , , XF Liao . . An extended method for obtaining S-boxes based on three-dimensional chaotic baker maps . . Chaos Sol Fract , , 2007 . . 31 ( ( 3 ): ): 571 - - 579 . . DOI: 10.1016/j.chaos.2005.10.022 http://doi.org/10.1016/j.chaos.2005.10.022 . .

JH Cheon , , , S Chee , , , C Park . . S-boxes with controllable nonlinearity . . Proc 17 th Int Conf on Theory and Application of Cryptographic Techniques , , 1999 . . p.286 - - 294 . . DOI: 10.1007/3-540-48910-X_20 http://doi.org/10.1007/3-540-48910-X_20 . .

NT Courtois , , , J Pieprzyk . . Cryptanalysis of block ciphers with overdefined systems of equations . . Proc 8 th Int Conf on Theory and Application of Cryptology and Information Security , , 2002 . . p.267 - - 287 . . DOI: 10.1007/3-540-36178-2_17 http://doi.org/10.1007/3-540-36178-2_17 . .

LG Cui , , , YD Cao . . A new S-box structure named affine- power-affine . . Int J Innov Comput Inform Contr , , 2007 . . 3 ( ( 3 ): ): 751 - - 759 . . . .

J Daemen , , , V Rijmen . . The Design of Rijndael-AES: the Advanced Encryption Standard . . Springer, Berlin, Germany , , 2002 . . .

P Devaraj , , , C Kavitha . . An image encryption scheme using dynamic S-boxes . . Nonl Dynam , , 2016 . . 86 ( ( 2 ): ): 927 - - 940 . . DOI: 10.1007/s11071-016-2934-7 http://doi.org/10.1007/s11071-016-2934-7 . .

A Gautam , , , GS Gaba , , , R Miglani , , , 等 . . Application of chaotic functions for construction of strong substitution boxes . . Ind J Sci Technol , , 2015 . . 8 ( ( 28 ): ): 1 - - 5 . . DOI: 10.17485/ijst/2015/v8i28/71759 http://doi.org/10.17485/ijst/2015/v8i28/71759 . .

U Hayat , , , NA Azam . . A novel image encryption scheme based on an elliptic curve . . Signal Process , , 2019 . . 155 391 - - 402 . . DOI: 10.1016/j.sigpro.2018.10.011 http://doi.org/10.1016/j.sigpro.2018.10.011 . .

U Hayat , , , NA Azam , , , M Asif . . A method of generating 8×8 substitution boxes based on elliptic curves . . Wirel Pers Commun , , 2018 . . 101 ( ( 1 ): ): 439 - - 451 . . DOI: 10.1007/s11277-018-5698-1 http://doi.org/10.1007/s11277-018-5698-1 . .

I Hussain , , , NA Azam , , , T Shah . . Stego optical encryption based on chaotic S-box transformation . . Opt Laser Technol , , 2014 . . 61 50 - - 56 . . DOI: 10.1016/j.optlastec.2014.01.018 http://doi.org/10.1016/j.optlastec.2014.01.018 . .

T Jakobsen , , , LR Knudsen . . The interpolation attack on block ciphers . . Proc 4 th Int Workshop on Fast Software Encryption , , 1997 . . p.28 - - 40 . . DOI: 10.1007/BFb0052332 http://doi.org/10.1007/BFb0052332 . .

S Katiyar , , , N Jeyanthi . . Pure dynamic S-box construction . . Int J Comput , , 2016 . . 1 42 - - 46 . . . .

K Kazlauskas , , , J Kazlauskas . . Key-dependent S-box generation in AES block cipher system . . Informatica , , 2009 . . 20 ( ( 1 ): ): 23 - - 34 . . . .

M Khan , , , NA Azam . . Right translated AES gray S-boxes . . Secur Commun Netw , , 2015a . . 8 1627 - - 1635 . . DOI: 10.1002/sec.1110 http://doi.org/10.1002/sec.1110 . .

M Khan , , , NA Azam . . S-boxes based on affine mapping and orbit of power function . . 3D Res , , 2015b . . 6 ( ( 2 ): ): Article 43 DOI: 10.1007/s13319-015-0043-x http://doi.org/10.1007/s13319-015-0043-x . .

J Kim , , , RCW Phan . . Advanced differential-style cryptanalysis of the NSA's skipjack block cipher . . Cryptologia , , 2009 . . 33 ( ( 3 ): ): 246 - - 270 . . DOI: 10.1080/01611190802653228 http://doi.org/10.1080/01611190802653228 . .

JM Liu , , , BD Wai , , , XG Cheng , , , 等 . . An AES S-box to increase complexity and cryptographic analysis . . Proc 19 th Int Conf on Advanced Information Networking and Applications , , 2005 . . p.724 - - 728 . . DOI: 10.1109/AINA.2005.84 http://doi.org/10.1109/AINA.2005.84 . .

Y Liu , , , J Wang , , , JH Fan , , , 等 . . Image encryption algorithm based on chaotic system and dynamic S-boxes composed of DNA sequences . . Multim Tools Appl , , 2016 . . 75 ( ( 8 ): ): 4363 - - 4382 . . DOI: 10.1007/s11042-015-2479-7 http://doi.org/10.1007/s11042-015-2479-7 . .

G Manjula , , , HS Mohan . . Constructing key dependent dynamic S-box for AES block cipher system . . Proc 2 nd Int Conf on Applied and Theoretical Computing and Communication Technology , , 2013 . . p.613 - - 617 . . DOI: 10.1109/ICATCCT.2016.7912073 http://doi.org/10.1109/ICATCCT.2016.7912073 . .

B Maram , , , JM Gnanasekar . . Evaluation of key dependent S-box based data security algorithm using Hamming distance and balanced output . . TEM J , , 2016 . . 5 ( ( 1 ): ): 67 - - 75 . . DOI: 10.18421/TEM51-11 http://doi.org/10.18421/TEM51-11 . .

W Meier , , , O Staffelbach . . Nonlinearity criteria for cryptographic functions . . Proc Advances in Cryptology— EUROCRYPT , , 1990 . . p.549 - - 562 . . DOI: 10.1007/3-540-46885-4_53 http://doi.org/10.1007/3-540-46885-4_53 . .

VS Miller . . Use of elliptic curves in cryptography . . Proc Advances in Cryptology—CRYPTO , , 1986 . . p.417 - - 426 . . DOI: 10.1007/3-540-39799-X_31 http://doi.org/10.1007/3-540-39799-X_31 . .

S Murphy , , , MJB Robshaw . . Essential algebraic structure within the AES . . Proc 22 nd Annual Int Cryptology Conf , , 2002 . . p.1 - - 16 . . DOI: 10.1007/3-540-45708-9_1 http://doi.org/10.1007/3-540-45708-9_1 . .

B Rahnama , , , Y Kıran , , , R Dara . . Countering AES static S-box attack . . Proc 6 th Int Conf on Security of Information and Networks , , 2013 . . p.256 - - 260 . . DOI: 10.1145/2523514.2523544 http://doi.org/10.1145/2523514.2523544 . .

J Rosenthal . . A polynomial description of the Rijndael advanced encryption standard . . J Algebr Appl , , 2003 . . 2 ( ( 2 ): ): 223 - - 236 . . DOI: 10.1142/S0219498803000532 http://doi.org/10.1142/S0219498803000532 . .

CE Shannon . . Communication theory of secrecy systems . . Bell Syst Tech J , , 1949 . . 28 ( ( 4 ): ): 656 - - 715 . . DOI: 10.1002/j.1538-7305.1949.tb00928.x http://doi.org/10.1002/j.1538-7305.1949.tb00928.x . .

GP Tang , , , XF Liao , , , Y Chen . . A novel method for designing S-boxes based on chaotic maps . . Chaos Sol Fract , , 2005 . . 23 ( ( 2 ): ): 413 - - 419 . . DOI: 10.1016/j.chaos.2004.04.023 http://doi.org/10.1016/j.chaos.2004.04.023 . .

MT Tran , , , DK Bui , , , AD Duong . . Gray S-box for advanced encryption standard . . Proc Int Conf on Computational Intelligence and Security , , 2008 . . p.253 - - 258 . . DOI: 10.1109/CIS.2008.205 http://doi.org/10.1109/CIS.2008.205 . .

XY Wang , , , Q Wang . . A novel image encryption algorithm based on dynamic S-boxes constructed by chaos . . Nonl Dynam , , 2014 . . 75 ( ( 3 ): ): 567 - - 576 . . DOI: 10.1007/s11071-013-1086-2 http://doi.org/10.1007/s11071-013-1086-2 . .

Y Wang , , , L Yang , , , M Li , , , 等 . . A method for designing S-box based on chaotic neural network . . Proc 6 th Int Conf on Natural Computation , , 2010 . . p.1033 - - 1037 . . DOI: 10.1109/ICNC.2010.5582968 http://doi.org/10.1109/ICNC.2010.5582968 . .

LC Washington . . Elliptic Curves: Number Theory and Cryptography , , 2 nd Ed. : : London, UK Chapman & Hall/CRC , , 2008 . . .

G Zaibi , , , A Kachouri , , , F Peyrard , , , 等 . . On dynamic chaotic S-Box . . Proc Global Information Infrastructure Symp , , 2009 . . p.1 - - 5 . . DOI: 10.1109/GIIS.2009.5307035 http://doi.org/10.1109/GIIS.2009.5307035 . .

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