Related papers: On weak differential uniformity of vectorial Boole…
Most modern block ciphers are built using components whose cryptographic strength is evaluated in terms of their resistance to attacks on the whole cipher. In particular, differential properties of vectorial Boolean functions are studied…
Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential…
Differential uniformity is a significant concept in cryptography as it quantifies the degree of security of S-boxes respect to differential attacks. Power functions of the form $F(x)=x^d$ with low differential uniformity have been…
Block ciphers use S-boxes to create confusion in the cryptosystems. Such S-boxes are functions over $\mathbb{F}_{2^{n}}$. These functions should have low differential uniformity, high nonlinearity, and high algebraic degree in order to…
We give a geometric characterization of vectorial boolean functions with differential uniformity less or equal to 4.
Vectorial Boolean functions are crucial building-blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria for vectorial Boolean functions, such as differential uniformity and…
S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved…
Vectorial Boolean functions are crucial building blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria of vectorial Boolean functions,such as differential distribution table…
We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of…
In this brief paper we introduce a robust-safety notion for differential inclusions, and we propose a general framework to certify such a notion in terms of barrier functions. While existing literature studied only what we designate by…
Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of more general statistical biases in the differences. To this…
Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of…
In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities…
Differentially 4-uniform permutations on $\gf_{2^{2k}}$ with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred…
We discuss the second-order differential uniformity of vectorial Boolean functions. The closely related notion of second-order zero differential uniformity has recently been studied in connection to resistance to the boomerang attack. We…
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a…
Substitution boxes (S-boxes) play a significant role in ensuring the resistance of block ciphers against various attacks. The Difference Distribution Table (DDT), the Feistel Boomerang Connectivity Table (FBCT), the Feistel Boomerang…
S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value,…
Traditional cryptography is suffering a huge threat from the development of quantum computing. While many currently used public-key cryptosystems would be broken by Shor's algorithm, the effect of quantum computing on symmetric ones is…
Testability of digital ICs rely on the principle of controllability and observability. Adopting conventional techniques like scan-chains open up avenues for attacks, and hence cannot be adopted in a straight-forward manner for security…