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Weights on affine subspaces and some other cryptographic characteristics of Boolean functions of 5 variables
Boolean functions affine classification nonlinearity algebraic degree
2019/5/27
Recently one new key recovery method for a filter generator was proposed. It is based on so-called planar approximations of such a generator. This paper contains the numerical part of the research of ...
A Note on Sub-Gaussian Random Variables
sub-Gaussians fully homomorphic encryption FHE boostrapping
2019/5/21
A sub-Gaussian distribution is any probability distribution that has tails bounded by a Gaussian and has a mean of zero. It is well known that the sum of independent sub-Gaussians is again sub-Gaussia...
Fast Algebraic Immunity of $2^m+2$ & $2^m+3$ variables Majority Function
Fast algebraic immunity Majority function Algebraic immunity
2019/3/20
Boolean functions used in some cryptosystems of stream ciphers should satisfy various criteria simultaneously to resist some known attacks. The fast algebraic attack (FAA) is feasible if one can find ...
Finding Ordinary Cube Variables for Keccak-MAC with Greedy Algorithm
Keccak Keccak-MAC ordinary cube variables
2018/9/6
In this paper, we present an alternative method to choose ordinary cube variables for Keccak-MAC. Firstly, we choose some good candidates for ordinary cube variables with key-independent conditions. T...
Statistical and Linear Independence of Binary Random Variables
Xiao-Massey lemma block cipher linear cryptanalysis
2017/5/23
Linear cryptanalysis makes use of statistical models that consider linear approximations over block cipher and random permutation as binary random variables. In this note we show that linear and stati...
The Multiplicative Complexity of Boolean Functions on Four and Five Variables
Affine transformation Boolean functions Circuit complexity
2015/12/23
A generic way to design lightweight cryptographic primitives is to construct simple rounds
using small nonlinear components such as 4x4 S-boxes and use these iteratively (e.g., PRESENT [1]
and SPONG...
Patterson-Wiedemann type functions on 21 variables with Nonlinearity greater than Bent Concatenation bound
Covering Radius First Order Reed-Muller Code Nonlinearity
2015/12/22
Nonlinearity is one of the most challenging combinatorial property in the domain of Boolean function research.
Obtaining nonlinearity greater than the bent concatenation bound for odd number of varia...
Obtaining and solving systems of equations in key variables only for the small variants of Obtaining and solving systems of equations in key variables only for the small variants of
Algebraic attack meet-in-the-middle attack AES
2009/6/9
This work is devoted to attacking the small scale variants of the
Advanced Encryption Standard (AES) via systems that contain only
the initial key variables. To this end, we introduce a system of eq...
Classification of Boolean Functions of 6 Variables or Less with Respect to Cryptographic Properties
Boolean Functions Cryptographic Properties
2009/3/27
This paper presents an efficient approach for classification of the affine equivalence classes of
cosets of the first order Reed-Muller code with respect to cryptographic properties such as correlati...
Rewriting Variables: the Complexity of Fast Algebraic Attacks on Stream Ciphers
Complexity Fast Algebraic Attacks Stream Ciphers
2009/3/25
Recently proposed algebraic attacks [AK03,CM03] and fast algebraic attacks [A04,C03] have provided the best analyses against some deployed LFSR-based ciphers. The process complexity is exponential in ...
There exist Boolean functions on n (odd) variables having nonlinearity > 2n−1 − 2 n−1 2 if and only if n > 7
Autocorrelation Boolean Functions Combinatorial Problems
2008/11/24
For the first time we find Boolean functions on 9 variables having nonlinearity
241, that remained as an open question in literature for almost three decades. Such
functions are discovered using a s...
The constructing of 3-resilient Boolean functions of 9 variables with nonlinearity 240
secret-key cryptography Boolean functions resiliency
2008/8/25
In this work we present a new way to construct 3-resilient Boolean functions of 9 variables
with nonlinearity 240. Such function have been discovered very recently in [1] and [2] by heuristic search....
Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on Odd Number of Variables
Algebraic Immunity Boolean Function Nonlinearity Nonsingular Matrix
2008/6/4
In this paper we present a theoretical construction of Rotation
Symmetric Boolean Functions (RSBFs) on odd number of variables
with maximum possible AI and further these functions are not symmetric...
Balanced Boolean Function on 13-variables having Nonlinearity strictly greater than the Bent Concatenation Bound
Keywords: Balancedness Boolean Function Nonlinearity
2008/5/30
Very recently, Kavut and Yucel identified 9-variable Boolean functions having
nonlinearity 242, which is currently the best known. However, any of these functions
do not contain any zero in the Wals...