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Construction of the optimal algebraic immunity Boolean functions with correlation immunity from transformation RSBFs

Jinglian Huang, S.A. Hamouda, M. Mirzaei, Z. Yu
2016 MATEC Web of Conferences  
On construction of rotation symmetric Boolean functions with the optimal algebraic immunity, we construct correlation immunity Boolean functions with the optimal algebraic immunity by translation transformation  ...  In this paper, we discuss the effect of the cryptographic properties of translation transformation rotation symmetric Boolean functions.  ...  Theorem 4 first looking for higher-order algebraic immune completely rotation symmetric Boolean function, on the basis of this again by translational transform to construct high order algebraic immunity  ... 
doi:10.1051/matecconf/20166103006 fatcat:67a7gisoyrcvhd3vwlthatxbae

The algebraic immunity and the optimal algebraic immunity functions of a class of correlation immune H Boolean functions

Jinglian Huang, Zhuo Wang, S.A. Hamouda, M. Mirzaei, Z. Yu
2016 MATEC Web of Conferences  
We put forward an efficient method to study the algebraic immunity of H Boolean functions with Hamming weight of , getting the existence of the higher-order algebraic immunity functions with correlation  ...  We also prove the existing problem of the above 2-order algebraic immunity functions and the optimal algebraic immunity functions.  ...  The algebraic immunity and optimal algebraic immunity functions of a class of correlation immune H Boolean functions We discuss the cryptographic properties of H Boolean functions ( ) f x with the Hamming  ... 
doi:10.1051/matecconf/20166103004 fatcat:c4w7q6hpqrggjgkqeaqgm3ul5y

The Annihilators and the Correlation Immunity of H Boolean Functions

Jinglian Huang, Zhuo Wang
2016 DEStech Transactions on Engineering and Technology Research  
We also arrive at the sufficient and necessary condition and the sufficient condition, which are the ones that H Boolean functions satisfy the compatibility of 1st-order algebraic immunity and m-order  ...  Using the derivative and the e-derivative defined by ourselves as research tools, we study the compatibility of algebraic immunity and correlation immunity of H Boolean functions with Hamming weight of  ...  We obtain the sufficient and necessary condition on the compatibility of m-order correlation immunity and 1st-order algebraic immunity for this kind of H Boolean functions.  ... 
doi:10.12783/dtetr/iect2016/3811 fatcat:ruf2v7xwlfgf7k4lpjaekhhfxa

1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity

Gang Han, Yu Yu, Xiangxue Li, Qifeng Zhou, Dong Zheng, Hui Li
2017 Security and Communication Networks  
., balancedness, good correlation immunity) are considered as important properties of Boolean functions for using in cryptographic primitives.  ...  Implementation results also show that they are almost perfect algebraic immune functions.  ...  Cryptographic criteria for Boolean functions include balancedness, algebraic degree, nonlinearity, and correlation immunity.  ... 
doi:10.1155/2017/6268230 fatcat:xrqvbci5uffkfexma5ohzkw34q

Evolving cryptographically sound boolean functions

Stjepan Picek, Domagoj Jakobovic, Marin Golub
2013 Proceeding of the fifteenth annual conference companion on Genetic and evolutionary computation conference companion - GECCO '13 Companion  
This paper explores the evolution of Boolean functions for a cryptographic usage, with genetic algorithms and genetic programming.  ...  The results indicate that it is possible to obtain high quality Boolean functions with algorithms that are not tailor-made for this purpose.  ...  For a Boolean function to have good cryptographic properties we want it to be balanced, with high nonlinearity, algebraic degree, algebraic immunity, correlation immunity, low absolute indicator and sum-of-square  ... 
doi:10.1145/2464576.2464671 dblp:conf/gecco/PicekJG13 fatcat:rnhtomagmvfpleqo7ykzaoxs2m

Alternative forms of representation of Boolean functions in Cryptographic Information Security Facilities [article]

Kushch Sergii
2015 arXiv   pre-print
The methods suggested in the project, exemplified by Cognate-form representations of Boolean functions, show that the use of alternative forms of representation of Boolean functions in forming of cryptographic  ...  An example of this is, in particular, the formation of cryptographic functions with the use of alternative forms of representation, namely Cognate-representation of Boolean functions.  ...  These include the bent-function, the correlation-immune functions, the algebraically-immune functions and the algebraic non-degenerate functions.  ... 
arXiv:1510.01083v1 fatcat:75yznqafcnf7bdayebdcybvr6e

A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions

Rahul Saha, Ganesan Geetha, Gulshan Kumar, William J. Buchanan, Tai-hoon Kim
2021 Applied Sciences  
Several previous studies were executed to analyze these characteristics of the cryptographic functions specifically for Boolean and symmetric functions.  ...  We observe that SRFG is efficient for cryptographic operations in terms of propagation and immunity features.  ...  High algebraic immunity is a required factor for cryptographic algorithms to prevent algebraic attacks.  ... 
doi:10.3390/app11178073 fatcat:nwisyqchpfdzlgwueudawnwx5a

Cryptographic Boolean functions: One output, many design criteria

Stjepan Picek, Domagoj Jakobovic, Julian F. Miller, Lejla Batina, Marko Cupic
2016 Applied Soft Computing  
Our research confirms previous results, but also sheds new insights on the effectiveness and comparison of different evolutionary algorithms for this problem.  ...  Boolean functions represent an important primitive in the design of various cryptographic algorithms.  ...  Acknowledgments This work was supported in part by the Technology Foundation STW (project 12624 -SIDES), The Netherlands Organization for Scientific Research NWO (project ProFIL 628.001.007) and the ICT  ... 
doi:10.1016/j.asoc.2015.10.066 fatcat:4l2gjsw6frc6zhwebmq5orhtva

Heuristic Methods of Hill Climbing of Cryptographic Boolean Functions

Illarion Moskovchenko, Mykola Pastukhov, Alexandr Kuznetsov, Tetiana Kuznetsova, Valeriia Prokopenko, Vitaliy Kropyvnytskyi
2018 2018 International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T)  
The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given.  ...  In this article, heuristic methods of hill climbing for cryptographic Boolean functions satisfying the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are  ...  Section 4 evaluates the properties of the gradient-lift method for the formation of high non-linear correlation-immune cryptographic Boolean functions.  ... 
doi:10.1109/infocommst.2018.8632017 fatcat:apdzmqptqbderetvuq7276tk7y

Constructions of vectorial Boolean functions with good cryptographic properties

Luyang Li, Weiguo Zhang
2016 Science China Information Sciences  
Up to now, many results have been given to obtain (n, m) functions with good cryptographic properties, for example: [3-5] and so on, but only a few [6, 7] can have SAO nonlinearity (nonlinearity larger  ...  The best affine and linear approximation attacks show that high nonlinearity is significant for designing cryptographically strong functions.  ...  The responsibility for scientific accuracy and content remains entirely with the authors.  ... 
doi:10.1007/s11432-015-0863-3 fatcat:uylw4di2vfeejmrowpso2kryoq

Algorithm 959

José Antonio Álvarez-Cubero, Pedro J. Zufiria
2016 ACM Transactions on Mathematical Software  
VBF is a collection of C++ classes designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective.  ...  The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated with VBF: it obtains the nonlinearity linearity distance, algebraic degree, linear  ...  Hence, so far suboptimal results have been mainly obtained via heuristic search; for example, for re = 9 the best-known nonlinearity result is 242 [Kavut and Yucel 2010] .  ... 
doi:10.1145/2794077 fatcat:4tgey4sslzbxjfly4t3sra6hc4

Cryptographically Significant Boolean Functions: Construction and Analysis in Terms of Algebraic Immunity [chapter]

Deepak Kumar Dalai, Kishan Chand Gupta, Subhamoy Maitra
2005 Lecture Notes in Computer Science  
For the first time, in this paper, we present a construction method to generate Boolean functions on n variables with highest possible algebraic immunity n 2 .  ...  The cryptographic property of a Boolean function, that resists algebraic attack, is known as Algebraic Immunity (AI).  ...  Claude Carlet for carefully reading our construction and providing a correction in the expression of f l+8 .  ... 
doi:10.1007/11502760_7 fatcat:eq5nx5qexjgjpg7pf7pu5wgvti

On construction of correlation-immune functions via minimal functions

Evgeny Konstantinovich Alekseev, E K Karelina, Oleg Aleksejevich Logachev
2018 Mathematical Aspects of Cryptography  
The use of correlation-immune functions in a cryptographic primitive may provide resistance against some key compromising methods.  ...  This paper proposes a method combining two basic approaches of solving this problem: iterative and a direct-search ones. Proposed method is based on minimal correlation-immune functions.  ...  The authors are grateful to Grigory Anatolyevich Karpunin, Grigory Borisovich Marshalko and Andrei Mihailovich Zubkov for their valuable comments and constructive criticism.  ... 
doi:10.4213/mvk251 fatcat:uitxw4vsqnd7joexp7rxlzm32a

Strengthening Crypto-1 Cipher Against Algebraic Attacks

Farah Afianti, Ari M. Barmawi
2015 Journal of ICT Research and Applications  
In order to strengthen Crypto-1 against SAT solver attacks, a modification of the feedback function with better cryptographic properties is proposed.  ...  SAT solvers cannot directly attack the feedback shift register that uses the modified Boolean feedback function, the register has to be split into smaller groups.  ...  Acknowledgements We would like to express our gratitude to the director and all lecturers of Telkom University, especially at the Master Training Program of the Graduate School, and friends for their moral  ... 
doi:10.5614/itbj.ict.res.appl.2015.9.1.5 fatcat:cxu5k3oaufdvtbo2yh7en5jube

Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables [article]

Na Li, Wen-feng Qi
2005 arXiv   pre-print
In this correspondence we prove that for each odd n, there is exactly one trivial balanced n-variable symmetric Boolean function achieving the algebraic immunity n/2 .  ...  And we also obtain a necessary condition for the algebraic normal form of a symmetric Boolean function with maximum algebraic immunity.  ...  It is important and significant to search or construct Boolean function with maximum algebraic immunity.  ... 
arXiv:cs/0511099v1 fatcat:4ruzmuvjnbgdregqarfcl2mudq
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