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Exceptional orthogonal Hermite and Laguerre polynomials have been linked to the k-step extension of harmonic and singular oscillators. The exceptional polynomials allow the existence of different supercharges from the Darboux-Crum and…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already…
This paper proposed the application of post-encryption-compression (PEC) to strengthen the secrecy in the case of distributed encryption where the encryption keys are correlated to each other. We derive the universal code construction for…
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the…
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels,…
In this short note, we develop a novel idea of a bilinear cryptosystem using the discrete logarithm problem in matrices. These matrices come from a linear representation of a finite $p$-group of class 2. We discuss an example at the end.
In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…
Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials…
With the advancement of quantum computing, symmetric cryptography faces new challenges from quantum attacks. These attacks are typically classified into two models: Q1 (classical queries) and Q2 (quantum superposition queries). In this…
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…
In this work, we introduce a symmetric algorithm obtained by the recurrence relation a_{n}^{k}=a_{n-1}^{k}+a_{n}^{k-1}. We point out that this algorithm can be apply to hyperharmonic-, ordinary and incomplete Fibonacci- and Lucas numbers.…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…
Over-parameterized neural language models (LMs) can memorize and recite long sequences of training data. While such memorization is normally associated with undesired properties such as overfitting and information leaking, our work casts…
This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions. The resulting codes achieve a higher error-correction performance at the same…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and…