Boolean Functions for Cryptography and Error-Correcting Codes
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.
Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems
- C. Carlet, P. Charpin, V. Zinoviev
- Computer Science, MathematicsDes. Codes Cryptogr.
- 1 November 1998
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
- C. Carlet, S. Guilley
- Computer ScienceAdvances in Mathematics of Communications
- 1 March 2016
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.
Algebraic Attacks and Decomposition of Boolean Functions
- W. Meier, E. Pasalic, C. Carlet
- Computer Science, MathematicsInternational Conference on the Theory and…
- 2 May 2004
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.
Vectorial Boolean Functions for Cryptography
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
- C. Carlet, K. Feng
- Computer Science, MathematicsInternational Conference on the Theory and…
- 7 December 2008
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.
Linear Codes Over 𝔽q Are Equivalent to LCD Codes for q>3
- C. Carlet, S. Mesnager, Chunming Tang, Yanfeng Qi, R. Pellikaan
- Computer ScienceIEEE Transactions on Information Theory
- 3 January 2018
A general construction of LCD codes from any linear codes is introduced and it is shown that any linear code over $\mathbb F_{q} (q>3)$ is equivalent to a Euclidean LCD code and anylinear code over $q^{2}(q>2)$ (q-ary linear codes) is equivalents to a Hermitian LCD code.
Two New Classes of Bent Functions
- C. Carlet
- Mathematics, Computer ScienceInternational Conference on the Theory and…
- 2 January 1994
A new class of bent functions on (GF(2)n ( n even) is introduced and it is proved that this class is not included in one of the known classes of bent function, and that, when n equals 6, it covers the whole set ofbent functions of degree 3.
Linear codes from perfect nonlinear mappings and their secret sharing schemes
In this paper, error-correcting codes from perfect nonlinear mappings are constructed, and then employed to construct secret sharing schemes. The error-correcting codes obtained in this paper are…
Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications
- C. Carlet
- Computer Science, MathematicsIEEE Transactions on Information Theory
- 1 March 2008
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).
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