# Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality

@inproceedings{Maitra1999HighlyNR, title={Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality}, author={Subhamoy Maitra and Palash Sarkar}, booktitle={CRYPTO}, year={1999} }

Siegenthaler proved that an n input 1 output, m-resilient (balanced mth order correlation immune) Boolean function with algebraic degree d satisfies the inequality : m + d ≤ n - 1. We provide a new construction method using a small set of recursive operations for a large class of highly nonlinear, resilient Boolean functions optimizing Siegenthaler's inequality m + d = n - 1. Comparisons to previous constructions show that better nonlinearity can be obtained by our method. In particular, we…

## 42 Citations

On the Coset Weight Divisibility and Nonlinearity of Resilient and Correlation-Immune Functions

- MathematicsSETA
- 2001

A bound on the nonlinearity of resilient functions involving n, m and d is deduced, which improves upon those given recently and independently by Sarkar and Maitra and by Tarannikov and stands in the more general framework of m-th order correlation-immune functions.

Construction of Nonlinear Boolean Functions with Important Cryptographic Properties

- Mathematics, Computer ScienceEUROCRYPT
- 2000

It is shown that for each positive integer m, there are infinitely many integers n, such that it is possible to construct n-variable, m-resilient functions having nonlinearity greater than 2n-1 -2[n/2].

On Boolean Functions with Low Polynomial Degree and Higher Order Sensitivity

- Computer Science, MathematicsArXiv
- 2021

This paper connects the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial degree and high sensitivity and presents a construction with low (n − ω(1) order sensitivity exploiting Maiorana-McFarland constructions, that is borrowed from construction of resilient functions.

BDD based construction of resilient functions

- Computer Science, Mathematics
- 2011

BDDs with attributed edges are made use of to provide an implementation of two construction meth- ods proposed by Maitra and Sakar and it is demonstrated that the size of BDDs of resilient functions obtained in this way grows linearly with the number of variables.

Construction of Highly Nonlinear Plateaued Resilient Functions with Disjoint Spectra

- Mathematics, Computer Science
- 2012

The nonlinearity of the constructed functions (for some functions) has improved upon the bounds obtained by Gao et al., and some new constructions of highly nonlinear resilient Boolean functions on large number of variables with disjoint spectra by concatenating disjointed spectra functions on small number of variable.

On Resilient Boolean Functions with Maximal Possible Nonlinearity

- Mathematics, Computer ScienceINDOCRYPT
- 2000

It is proved that the maximal possible nonlinearity of n- variable m-resilient Boolean function is 2n-1-2m+1 for 2n-7/ 3 ≤ m ≤ n-2. This value can be achieved only for optimized functions (i. e.…

On Nonlinearity and Autocorrelation Properties of Correlation Immune Boolean Functions

- Computer Science, MathematicsJ. Inf. Sci. Eng.
- 2004

This paper provides a construction method for unbalanced, first order correlation immune Boolean functions on even an number of variables n ≥ 6, and points out the weakness of two recursive construction techniques for resilient functions in terms of autocorrelation values.

On Cryptographic Properties of the Cosets of

- Computer Science
- 2001

A new approach for the study of weight distributions of cosets of the Reed-Muller code of order is introduced, based on the method introduced by Kasami in (1), using Pless identities to obtain a condition for a coset to have a "high" minimum weight.

Cryptographically significant Boolean functions with five valued Walsh spectra

- Computer Science, MathematicsTheor. Comput. Sci.
- 2002

A Maiorana-McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity >2n-1-2n/2+2n/2-2

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2006

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