Related papers: The regular multivariate quadratic problem
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…
Current quantum computers can only solve optimization problems of a very limited size. For larger problems, decomposition methods are required in which the original problem is broken down into several smaller sub-problems. These are then…
Quantum signal processing (QSP) is a highly successful algorithmic primitive in quantum computing which leads to conceptually simple and efficient quantum algorithms using the block-encoding framework of quantum linear algebra. Multivariate…
In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be…
This paper proposes a new block cipher termed as "Modular Arithmetic based Block Cipher with Varying Key-Spaces (MABCVK)" that uses private key-spaces of varying lengths to encrypt data files. There is a simple but intelligent use of theory…
Differential cryptanalysis is one of the most popular methods in attacking block ciphers. However, there still some limitations in traditional differential cryptanalysis. On the other hand, researches of quantum algorithms have made great…
In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
We study the problem of computing matrix chain multiplications in a distributed computing cluster. In such systems, performance is often limited by the straggler problem, where the slowest worker dominates the overall computation latency.…
One of the challenging scientific computing problems is topology optimization, where searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously.…
Block ciphers are in widespread use since the 1970s. Their iterated structure is prone to numerous round invariant attacks for example in Linear Cryptanalysis (LC). The next step is to look at non-linear polynomial invariants cf.…
Solving a system of $m$ multivariate quadratic equations in $n$ variables over finite fields (the MQ problem) is one of the important problems in the theory of computer science. The XL algorithm (XL for short) is a major approach for…
We consider the problem of secure distributed matrix multiplication (SDMM). Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against workers and boosting the…
We study separable plus quadratic (SPQ) polynomials, i.e., polynomials that are the sum of univariate polynomials in different variables and a quadratic polynomial. Motivated by the fact that nonnegative separable and nonnegative quadratic…
The NP-hardness of the closest vector problem (CVP) is an important basis for quantum-secure cryptography, in much the same way that integer factorisation's conjectured hardness is at the foundation of cryptosystems like RSA. Recent work…
In this paper we study the long-standing open question regarding the computational complexity of one of the core problems in supply chains management, the periodic joint replenishment problem. This problem has received a lot of attention…
Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital documents. In the post-quantum era, classical public key-based signature schemes become vulnerable to brute-force and…
A continuous variable controlled quantum dialogue scheme is proposed. The scheme is further modified to obtain two other protocols of continuous variable secure multiparty computation. The first one of these protocols provides a solution of…
Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of…
The Bivariate Function Hard Problem (BFHP) has been in existence implicitly in almost all number theoretic based cryptosystems. This work defines the BFHP in a more general setting and produces an efficient asymmetric cryptosystem. The…