Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity

This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler＇s upper bound of algebraic degree. Also a class of l-resilient functions on any number n 〉 2 of variables with at least sub-optimal algebraic immunity is provided.

A Combinatorial Condition and Boolean Functions with Optimal Algebraic Immunity

This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.

Construction of Balanced Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity

Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.

Further results on differentially 4-uniform permutations over F2^2m

We present several new constructions of differentially 4-uniform permutations over F22 mby modifying the values of the inverse function on some subsets of F22 m. The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of crytographic substitution boxes.

Known-key distinguishers on type-1 Feistel scheme and near-collision attacks on its hashing modes

We present some known-key distinguishers for a type-1 Feistel scheme with a permutation as the round function. To be more specific, the 29-round known-key truncated differential distinguishers are given for the 256-bit type-1 Feistel scheme with an SP （substitution-permutation） round function by using the rebound attack, where the S-boxes have perfect differential and linear properties and the linear diffusion layer has a maximum branch number. For two 128-bit versions, the distinguishers can be applied on 25- round structures. Based on these distinguishers, we construct near-collision attacks on these schemes with MMO （Matyas- Meyer-Oseas） and MP （Miyaguchi-Preneel） hashing modes, and propose the 26-round and 22-round near-collision attacks for two 256-bit schemes and two 128-bit schemes, respectively. We apply the near-collision attack on MAME and obtain a 26-round near-collision attack. Using the algebraic degree and some integral properties, we prove the correctness of the 31-round known-key integral distinguisher proposed by Sasaki et al. We show that if the round function is a permutation, the integral distinguisher is suitable for a type-1 Feistel scheme of any size.

A new family of differentially 4-uniform permutations over F_(2^(2k))for odd k

We study the differential uniformity of a class of permutations over F2 n with n even. These permutations are different from the inverse function as the values x^(-1) are modified to be(γx)^(-1) on some cosets of a fixed subgroup γ of F_(2n)~*. We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent(CCZ-equivalent) classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.

Non-Monomial Permutations with Differential Uniformity Six

In this paper, a family of non-monomial permutations over the finite field F2n with differential uniformity at most 6 is proposed, where n is a positive integer. The algebraic degree of these functions is also determined.