# Highly Nonlinear Balanced Boolean Functions with a Good Correlation-Immunity

@inproceedings{Filiol1998HighlyNB, title={Highly Nonlinear Balanced Boolean Functions with a Good Correlation-Immunity}, author={Eric Filiol and Caroline Fontaine}, booktitle={EUROCRYPT}, year={1998} }

We study a corpus of particular Boolean functions: the idempotents. They enable us to construct functions which achieve the best possible tradeoffs between the cryptographic fundamental properties: balancedness, correlation-immunity, a high degree and a high nonlinearity (that is a high distance from the affine functions). They all represent extremely secure cryptographic primitives to be implemented in stream ciphers.

## 133 Citations

Further Results on the Relation Between Nonlinearity and Resiliency for Boolean Functions

- Computer Science, MathematicsIMACC
- 1999

This paper establishes the maximum non linearity for a fixed resiliency in certain cases and presents a simple search algorithm for finding Boolean functions with good nonlinearity and some fixed Resiliency.

Further constructions of resilient Boolean functions with very high nonlinearity

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 2002

A design of good combining Boolean functions that provide resilient Boolean functions with currently best known nonlinearity and achieve the provable upper bound on non linearity for resilience Boolean functions.

A Brief Outline of Research on Correlation Immune Functions

- Computer Science, MathematicsACISP
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This paper outlines the development in the field of constructing correlation immune Boolean functions with high nonlinearity and algebraic degree and briefly survey related issues in this area.

Two New Constructions of Resilient Boolean Functions Satisfying Propagation Criterion

- Mathematics
- 2000

Recently the relationships among cryptographic criteria of boolean functions, including balancedness, the algebraic degree, nonlinearity, propagation criterion and correlation immunity, have been…

Evolving Highly Nonlinear Balanced Boolean Functions with Improved Resistance to DPA Attacks

- Computer Science, MathematicsNSS
- 2015

Three 8-bit highly nonlinear balanced Boolean functions have been evolved in this work that have higher DPA resistance than others published previously.

Boolean functions with all main cryptographic properties

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2010

A class of 2k-variable Boolean functions which have optimal algebraic degree, very high nonlinearity, and are 1-resilient is proposed, and it can be shown that the algebraic immunity of these functions is at least suboptimal.

Results on Algebraic Immunity for Cryptographically Significant Boolean Functions

- Computer Science, MathematicsINDOCRYPT
- 2004

It is shown that high nonlinearity is a necessary condition to resist algebraic attack and how the Walsh spectra values are related to the algebraic immunity (resistance against algebraic attacked) of a Boolean function is explained.

Propagation Characteristics and Correlation-Immunity of Highly Nonlinear Boolean Functions

- MathematicsEUROCRYPT
- 2000

It is proved that highly nonlinear functions usually have good propagation properties regarding different criteria and that most highly non linear functions with a three-valued Walsh spectrum can be transformed into 1-resilient functions.

Ciphertext Only Reconstruction of Stream Ciphers Based on Combination Generators

- Mathematics, Computer ScienceFSE
- 2000

An operational reconstruction technique of most stream ciphers is presented, primarily exposed for key-stream generators which consist of several linear feedback shift registers combined by a nonlinear Boolean function.

Nonlinearity Measures of Boolean Functions

- Mathematics, Computer Science
- 2016

These properties of Boolean functions, including algebraic degree, linear structure property, and higher-order nonlinearity, are extensively studied in this chapter.

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