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Upper Bounds on Algebraic Immunity of Boolean Power Functions
[chapter]
2006
Lecture Notes in Computer Science
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We give an upper bound on the AI of any Boolean power function and a formula to find its corresponding low degree multiples. ...
The function used in a symmetric cipher should have high algebraic immunity (AI) to resist algebraic attacks. In this paper we are interested in finding AI of Boolean power functions. ...
For example we derive upper bounds on the AI of many Boolean power functions that are much lower than the optimal upper bound presented in literature. ...
doi:10.1007/11799313_24
fatcat:pc33o324dzaatlplmd7f7bctte
New Constructions of Balanced Boolean Functions with Maximum Algebraic Immunity, High Nonlinearity and Optimal Algebraic Degree
2020
Walailak Journal of Science and Technology
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This paper consists of proposal of two new constructions of balanced Boolean function achieving a new lower bound of nonlinearity along with high algebraic degree and optimal or highest algebraic immunity ...
The constructed balanced variable Boolean functions achieve higher nonlinearity, algebraic degree of , and algebraic immunity of for odd , for even . ...
Then, the concept of algebraic immunity was introduced in [6] . The algebraic immunity of a Boolean function should be high to resist the standard algebraic attack. ...
doi:10.48048/wjst.2020.5999
fatcat:vgciyz44ybeh3obpw5jlqeh7ce
Perfect Algebraic Immune Functions
[chapter]
2012
Lecture Notes in Computer Science
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The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of ...
A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. ...
The first author would like to thank Dingyi Pei for his enlightening conversations on the resistance of Boolean functions against algebraic attacks. ...
doi:10.1007/978-3-642-34961-4_12
fatcat:f25zqpqnczbfvbyh6azklosdt4
On the confusion coefficient of Boolean functions
2021
Journal of Mathematical Cryptology
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In this article, we establish a relationship between the confusion coefficient and the autocorrelation function for any Boolean function and give a tight upper bound and a tight lower bound on the confusion ...
We also deduce some deep relationships between the sum-of-squares of the confusion coefficient and other cryptographic indicators (the sum-of-squares indicator, hamming weight, algebraic immunity and correlation ...
Conflict of interest: Authors state no conflict of interest. ...
doi:10.1515/jmc-2021-0012
fatcat:5mbbk6f6f5bf7ljok3ivyaenlq
A New Upper Bound on the Block Error Probability After Decoding Over the Erasure Channel
2006
IEEE Transactions on Information Theory
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With this result, we also get an asymptotic lower bound on the algebraic immunity of a balanced random Boolean function. This is our Theorem 3.
VI. ...
For a -variable Boolean function, the algebraic immunity is always smaller than . ...
doi:10.1109/tit.2006.881719
fatcat:bkrn6te4zzbsngqyf3pr6xakhy
An Upper Bound on the Number of m-Resilient Boolean Functions
[chapter]
2002
Lecture Notes in Computer Science
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The enumeration of m-resilient Boolean functions in n variables would be a quite useful information for cryptography. But it seems to be an intractable open problem. ...
Upper and lower bounds have appeared in the literature in the mid 80 s. Since then, improving them has been the goal of several papers. ...
The first bounds on the number of first order correlation-immune Boolean functions were lower bounds (see [7, 14, 8, 5] ). In 1990, Yang and Guo published the first upper bound on such functions. ...
doi:10.1007/3-540-36178-2_30
fatcat:q7zuqjsmlfecdct43qmgw23clm
Construction of Odd-Variable Resilient Boolean Functions with Optimal Degree
2011
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
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Finally, the algebraic immunity and immunity against fast algebraic attack of the obtained Boolean functions are investigated. ...
In this paper, we investigate the problem of obtaining new construction methods for resilient Boolean functions. ...
Let us now clearly clarify the exact upper bounds on the nonlinearity of resilient Boolean functions. ...
doi:10.1587/transfun.e94.a.265
fatcat:ftx57hxec5cbbe6jefs352bw4a
Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions
2011
IEEE Transactions on Information Theory
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2009 pre-print arXiv:0910.4632v1 fatcat:6qgpffcjxfhttbzdqatfy7xedu
Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions. ...
A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. ...
Therefore the bound of Corollary 17 is tight. Notice that the relation between algebraic degree and algebraic immunity of symmetric Boolean functions doesn't relate to the number of variables. ...
doi:10.1109/tit.2011.2145690
fatcat:fsq22z5hyjeuff63egzsnforge
Boolean functions with restricted input and their robustness; application to the FLIP cipher
2017
IACR Transactions on Symmetric Cryptology
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We study the main cryptographic features of Boolean functions (balancedness, nonlinearity, algebraic immunity) when, for a given number n of variables, the input to these functions is restricted to some ...
We study in particular the case when E equals the set of vectors of fixed Hamming weight, which plays a role in the FLIP stream cipher and we study the robustness of the Boolean function in this cipher ...
Algebraic Immunity In this part we study the criterion of algebraic immunity on restricted inputs; first we study the bound on the maximal algebraic immunity reachable by a function on a restricted set ...
doi:10.13154/tosc.v2017.i3.192-227
dblp:journals/tosc/CarletMR17
fatcat:prtyvevlprdgpku4pxazoyfbta
Boolean functions with restricted input and their robustness; application to the FLIP cipher
2017
IACR Transactions on Symmetric Cryptology
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We study the main cryptographic features of Boolean functions (balancedness, nonlinearity, algebraic immunity) when, for a given number n of variables, the input to these functions is restricted to some ...
subset E of ...
Algebraic Immunity In this part we study the criterion of algebraic immunity on restricted inputs; first we study the bound on the maximal algebraic immunity reachable by a function on a restricted set ...
doi:10.46586/tosc.v2017.i3.192-227
fatcat:n7y3plebevb7zkp523tegk72ne
Fast algebraic immunity of Boolean functions and LCD codes
[article]
2020
arXiv
pre-print
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The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. ...
Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. ...
Using the definition above, an upper bound of fast algebraic immunity of power functions has been established by Mesnager and Cohen [34] . ...
arXiv:2006.08372v1
fatcat:5vgxykilvjbelc63eidathbwmq
A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity
2010
Designs, Codes and Cryptography
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the first class of functions are also bent, moreover, from this fact we conclude that the algebraic immunity of bent functions can take all possible values except one. ...
In this paper, we propose a combinatoric conjecture on binary string, on the premise that our conjecture is correct we mainly obtain two classes of functions which are both algebraic immunity optimal: ...
We are interested in the tight upper bound of nonlinearity of boolean functions with given algebraic immunity. ...
doi:10.1007/s10623-010-9413-9
fatcat:gardevyt3vfwrcxheasvg5cg2i
On Algebraic Immunity and Annihilators
[chapter]
2006
Lecture Notes in Computer Science
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Algebraic immunity AI(f ) defined for a boolean function f measures the resistance of the function against algebraic attacks. ...
This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI * (f ). ...
For any boolean function f on (GF (2)) n , the extended algebraic immunity of f is upper-bounded by its transversal number, i.e.,
Theorem 5 . 5 Let f be a 0-CM boolean function on (GF (2)) n satisfying ...
doi:10.1007/11927587_8
fatcat:rn22db5tdvedfknbv25piiem4u
Cryptographic Boolean functions: One output, many design criteria
2016
Applied Soft Computing
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Boolean functions represent an important primitive in the design of various cryptographic algorithms. ...
In this paper, we present three different objective functions, where each examines important cryptographic properties of Boolean functions, and examine four evolutionary algorithms. ...
The algebraic immunity is upper bounded by the number of input variables, more precisely [46] : AI ≤ n 2 . (17) Therefore, in the third objective we aim to find Boolean functions that are suitable for ...
doi:10.1016/j.asoc.2015.10.066
fatcat:4l2gjsw6frc6zhwebmq5orhtva
Constructing 2m-variable Boolean functions with optimal algebraic immunity based on polar decomposition of F_2^2m^*
[article]
2013
arXiv
pre-print
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Based on polar decomposition of the multiplicative group of F_2^2m, we propose a new construction of Boolean functions with optimal algebraic immunity. ...
Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field F_2^2m seems to be a promising approach since Tu and Deng's work. ...
It can be proved that the best possible value of the algebraic immunity of n-variable Boolean functions is ⌈ n 2 ⌉ [7] , thus functions attaining this upper bound are often known as algebraic immunity ...
arXiv:1304.2946v1
fatcat:pp2kqqajwnelfcfvn62xkizfay
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