Related papers: On weak differential uniformity of vectorial Boole…
In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…
Every day, millions of credit cards are swiped and transactions are carried out across the world. Due to numerous forms of unethical digital activities, users are vulnerable to credit card fraud, phishing, identity theft, etc. This paper…
Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially-4 uniform function called…
Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or…
In this paper we generalize Dillon's switching method to characterize the exact $c$-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known $c$-differential…
Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…
This paper addresses the problem of determining the minimum set of state variables in a network that need to be blocked from direct measurements in order to protect functional privacy with respect to {\emph{any}} output matrices. The goal…
When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well…
The seminal result of Impagliazzo and Rudich (STOC 1989) gave a black-box separation between one-way functions and public-key encryption: informally, a public-key encryption scheme cannot be constructed using one-way functions as the sole…
This paper generalizes the control barrier function framework by replacing scalar-valued functions with matrix-valued ones. Specifically, we develop barrier conditions for safe sets defined by matrix inequalities -- both semidefinite and…
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…
We defined in~\cite{EFRST20} a new multiplicative $c$-differential, and the corresponding $c$-differential uniformity and we characterized the known perfect nonlinear functions with respect to this new concept, as well as the inverse in any…
In this paper, we consider the problem of verifying safety constraint satisfaction for single-input single-output systems with uncertain transfer function coefficients. We propose a new type of barrier function based on a vector norm. This…
The Feistel Boomerang Connectivity Table ($\rm{FBCT}$), which is the Feistel version of the Boomerang Connectivity Table ($\rm{BCT}$), plays a vital role in analyzing block ciphers' ability to withstand strong attacks, such as boomerang…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
This paper establishes the equivalence between robust safety and the existence of a barrier function certificate for differential inclusions. More precisely, for a robustly-safe differential inclusion, a barrier function is constructed as…
Substitution boxes (S-boxes) play a significant role in ensuring the resistance of block ciphers against various attacks. The Upper Boomerang Connectivity Table (UBCT), the Lower Boomerang Connectivity Table (LBCT) and the Double Boomerang…