Related papers: Wave-Shaped Round Functions and Primitive Groups
We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field $\GF (p^k)$ ($p\geq 2$ a prime number) is not closed under functional composition.…
Encryption techniques demonstrate a great deal of security when implemented in an optical system (such as holography) due to the inherent physical properties of light and the precision it demands. However, such systems have shown to be…
Modern deep neural networks comprise many operational layers, such as dense or convolutional layers, which are often collected into blocks. In this work, we introduce a new, wavelet-transform-based network architecture that we call the…
We propose a reconstruction of vortex beams based on the implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the…
For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial…
A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters may send a possibly private message to the other transmitter in a cooperation phase before both transmitters…
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…
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…
We provide two sufficient conditions to guarantee that the round functions of a translation based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and…
Regenerating codes are a class of codes for distributed storage networks that provide reliability and availability of data, and also perform efficient node repair. Another important aspect of a distributed storage network is its security.…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
This article presents a new algorithm to find MDS matrices that are well suited for use as a diffusion layer in lightweight block ciphers. Using an recursive construction, it is possible to obtain matrices with a very compact description.…
Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations. Leinaas and Myrheim proposed how a fermionic wave function can be represented as a function of…
Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are…
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…
In this paper, we study applications of Bernstein-Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it,…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
In a functional encryption (FE) scheme, a user that holds a ciphertext and a function key can learn the result of applying the function to the plaintext message. Security requires that the user does not learn anything beyond the function…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a…