Evolving Nonlinear S-Boxes With Improved Theoretical Resilience to Power Attacks

Substitution boxes are the main nonlinear component of block ciphers. The security of these ciphers against linear, differential, or side-channel attacks is dependent on the design of such component and their intrinsic properties. There are several methods that aim to cryptographically define, generate, or search for strong substitution boxes. The application of combinatorial optimization algorithms is one of the most useful methodologies in this research area. In this article, we present a novel hybrid method based on the Leaders and Followers and hill-climbing over Hamming Weight Classes metaheuristics, coupled with a new trade-off fitness function that generates 8-bit bijective substitution boxes with good resisting properties towards classical cryptanalysis and side-channel attacks by power consumption. We address the best Pareto optimal solutions for the multi-objective optimization of non-linearity and confusion coefficient variance.

[1]  Ikram Ullah,et al.  Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field , 2018, Frontiers of Information Technology & Electronic Engineering.

[2]  Vincent Rijmen,et al.  The Design of Rijndael: AES - The Advanced Encryption Standard , 2002 .

[3]  Musheer Ahmad,et al.  Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures , 2020, IEEE Access.

[4]  Muhammad Fahad Khan,et al.  A Novel Cryptographic Substitution Box Design Using Gaussian Distribution , 2019, IEEE Access.

[5]  Ikram Ullah,et al.  An Injective S-Box Design Scheme over an Ordered Isomorphic Elliptic Curve and Its Characterization , 2018, Secur. Commun. Networks.

[6]  William Millan,et al.  How to Improve the Nonlinearity of Bijective S-Boxes , 1998, ACISP.

[7]  Susan Stepney,et al.  Searching for cost functions , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[8]  Jean-Didier Legat,et al.  ICEBERG : An Involutional Cipher Efficient for Block Encryption in Reconfigurable Hardware , 2004, FSE.

[9]  Siva Sai Yerubandi,et al.  Differential Power Analysis , 2002 .

[10]  Roman Oliynykov,et al.  A Method For Generation Of High-Nonlinear S-Boxes Based On Gradient Descent , 2013, IACR Cryptol. ePrint Arch..

[11]  Reynier Antonio de la Cruz Jiménez,et al.  Generation of 8-Bit S-Boxes Having Almost Optimal Cryptographic Properties Using Smaller 4-Bit S-Boxes and Finite Field Multiplication , 2017, LATINCRYPT.

[12]  세르게 바우덴이,et al.  Device and method for encrypting and decrypting a block of data , 2004 .

[13]  Olivier Markowitch,et al.  Comparing Sboxes of ciphers from the perspective of side-channel attacks , 2016, 2016 IEEE Asian Hardware-Oriented Security and Trust (AsianHOST).

[14]  Claude Carlet,et al.  PICARO - A Block Cipher Allowing Efficient Higher-Order Side-Channel Resistance , 2012, ACNS.

[15]  Majid Khan,et al.  An efficient method for the construction of block cipher with multi-chaotic systems , 2013 .

[16]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

[17]  Vincent Rijmen,et al.  The KHAZAD Legacy-Level Block Cipher , 2001 .

[18]  Debdeep Mukhopadhyay,et al.  Redefining the transparency order , 2015, Designs, Codes and Cryptography.

[19]  Miroslav Dimitrov On the Design of Chaos-Based S-Boxes , 2020, IEEE Access.

[20]  Kostas Papagiannopoulos,et al.  Confused by Confusion: Systematic Evaluation of DPA Resistance of Various S-boxes , 2014, INDOCRYPT.

[21]  Kaisa Nyberg,et al.  On the Construction of Highly Nonlinear Permutations , 1992, EUROCRYPT.

[22]  Congxu Zhu,et al.  An Efficient Image Encryption Scheme Based on the LSS Chaotic Map and Single S-Box , 2020, IEEE Access.

[23]  María Naya-Plasencia,et al.  Block Ciphers That Are Easier to Mask: How Far Can We Go? , 2013, CHES.

[24]  Ahmed A. Abd El-Latif,et al.  A novel image steganography technique based on quantum substitution boxes , 2019, Optics & Laser Technology.

[25]  Svetla Nikova,et al.  Reversed genetic algorithms for generation of bijective s-boxes with good cryptographic properties , 2016, Cryptography and Communications.

[26]  Claude Carlet,et al.  New classes of almost bent and almost perfect nonlinear polynomials , 2006, IEEE Transactions on Information Theory.

[27]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

[28]  Domagoj Jakobovic,et al.  One property to rule them all?: on the limits of trade-offs for S-boxes , 2020, GECCO.

[29]  Claude Carlet,et al.  Trade-Offs for S-Boxes: Cryptographic Properties and Side-Channel Resilience , 2017, ACNS.

[30]  Stjepan Picek,et al.  A New Cost Function for Evolution of S-Boxes , 2016, Evolutionary Computation.

[31]  Yongbin Zhou,et al.  The Notion of Transparency Order, Revisited , 2020, IACR Cryptol. ePrint Arch..

[32]  Svetla Nikova,et al.  Cryptographically Strong S-Boxes Generated by Modified Immune Algorithm , 2015, BalkanCryptSec.

[33]  Antonio Bolufé Röhler,et al.  Machine learning based metaheuristic hybrids for S-box optimization , 2020, J. Ambient Intell. Humaniz. Comput..

[34]  Petr Tesa A New Method for Generating High Non-linearity S-Boxes , 2010 .

[35]  Claude Carlet,et al.  Vectorial Boolean Functions for Cryptography , 2006 .

[36]  Susan Stepney,et al.  The design of S-boxes by simulated annealing , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[37]  Sylvain Guilley,et al.  A Theoretical Study of Kolmogorov-Smirnov Distinguishers: Side-Channel Analysis vs. Differential Cryptanalysis , 2014, IACR Cryptol. ePrint Arch..

[38]  Yasser González-Fernández,et al.  Leaders and followers — A new metaheuristic to avoid the bias of accumulated information , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[39]  Musheer Ahmad,et al.  A Novel Ant Colony Optimization Based Scheme for Substitution Box Design , 2015 .

[40]  Musheer Ahmad,et al.  Particle Swarm Optimization Based Highly Nonlinear Substitution-Boxes Generation for Security Applications , 2020, IEEE Access.

[41]  Kostas Papagiannopoulos,et al.  Optimality and beyond: The case of 4×4 S-boxes , 2014, 2014 IEEE International Symposium on Hardware-Oriented Security and Trust (HOST).

[42]  A. Adam Ding,et al.  A Statistical Model for DPA with Novel Algorithmic Confusion Analysis , 2012, CHES.

[43]  William Millan,et al.  Evolutionary Heuristics for Finding Cryptographically Strong S-Boxes , 1999, ICICS.

[44]  Yong Wang,et al.  A genetic algorithm for constructing bijective substitution boxes with high nonlinearity , 2020, Inf. Sci..

[45]  Majid Khan,et al.  A new construction of confusion component of block ciphers , 2019, Multimedia Tools and Applications.

[46]  Majid Khan,et al.  Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps , 2019, International Journal of Theoretical Physics.

[47]  Liwei Zhang,et al.  A Statistical Model for Higher Order DPA on Masked Devices , 2014, IACR Cryptol. ePrint Arch..

[48]  Fatih Özkaynak,et al.  Side-Channel Analysis of Chaos-Based Substitution Box Structures , 2019, IEEE Access.

[49]  Claude Carlet,et al.  Intrinsic Resiliency of S-Boxes Against Side-Channel Attacks–Best and Worst Scenarios , 2021, IEEE Transactions on Information Forensics and Security.