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Boolean Functions for Cryptography and Error-Correcting Codes
TLDR
Encryption-decryption is the most ancient cryptographic activity, but its nature has deeply changed with the invention of computers, because the cryptanalysis (the activity of the third person, the eavesdropper, who aims at recovering the message) can use their power.
Algebraic Attacks and Decomposition of Boolean Functions
TLDR
Algebraic attacks on LFSR-based stream ciphers recover the secret key by solving an overdefined system of multivariate algebraic equations and become very efficient if such relations of low degrees may be found.
Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems
TLDR
The "coding theory" point of view for studying the existence of almost bent functions is developed, showing explicitly the links with cyclic codes and new characterizations are given by means of associated Boolean functions.
Complementary dual codes for counter-measures to side-channel attacks
TLDR
It is recalled why linear codes with complementary duals (LCD codes) play a role in counter-measures to passive and active side-channel analyses on embedded cryptosystems and constructions are investigated.
Vectorial Boolean Functions for Cryptography
TLDR
To appear as a chapter of the volume " Boolean Methods and Models " , this chapter describes the construction of Boolean models and some examples show how to model Boolean functions using LaSalle's inequality.
An Infinite Class of Balanced Functions with Optimal Algebraic Immunity, Good Immunity to Fast Algebraic Attacks and Good Nonlinearity
TLDR
It is proved that an infinite class of functions which achieve an optimum algebraic degree and a much better nonlinearity than all the previously obtained infinite classes of functions have a very good non linearity and also a good behavior against fast algebraic attacks.
Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications
  • C. Carlet
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 1 March 2008
TLDR
This work deduces bounds on the second-order nonlinearity for several classes of cryptographic Boolean functions, including the Welch and the multiplicative inverse functions (used in the S-boxes of the Advanced Encryption Standard (AES).
Highly nonlinear mappings
TLDR
A well-rounded treatment of non-Boolean functions with optimal nonlinearity is given, which summarizes and generalizes known results, and proves a number of new results.
Z2k-Linear Codes
  • C. Carlet
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 1 July 1998
TLDR
A generalization to Z/sub 2/k, of the Gray map and generalized versions of Kerdock and Delsarte-Goethals codes are introduced.
Highly Nonlinear Boolean Functions With Optimal Algebraic Immunity and Good Behavior Against Fast Algebraic Attacks
TLDR
The infinite class of functions proposed in Construction 2 presents, among all currently known constructions, the best provable tradeoff between all the important cryptographic criteria.
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