相关论文: Secure Montgomery Multiplication and Repeated Squa…
The factorization of a large digit integer in polynomial time is a challenging computational task to decipher. The exponential growth of computation can be alleviated if the factorization problem is changed to an optimization problem with…
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…
Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…
In this paper, we propose a novel construction for secure distributed matrix multiplication (SDMM) based on algebraic geometry (AG) codes, which we call the PoleGap SDMM scheme. The proposed construction is inspired by the GASP code, where…
This paper is about solving polynomial systems. It first recalls how to do that efficiently with a very high probability of correctness by reconstructing a rational univariate representation (rur) using Groebner revlex computation,…
In their 2022 study, Kuang et al. introduced Multivariable Polynomial Public Key (MPPK) cryptography, leveraging the inversion relationship between multiplication and division for quantum-safe public key systems. They extended MPPK into…
Some pioneering works have investigated embedding cryptographic properties in compressive sampling (CS) in a way similar to one-time pad symmetric cipher. This paper tackles the problem of constructing a CS-based symmetric cipher under the…
This paper presents software implementations of batch computations, dealing with multi-precision integer operations. In this work, we use the Single Instruction Multiple Data (SIMD) AVX512 instruction set of the x86-64 processors, in…
Intelligent reflecting surfaces (IRSs) have shown huge advantages in many potential use cases and thus have been considered a promising candidate for next-generation wireless systems. In this paper, we consider an IRS-assisted multigroup…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
While Attention Residuals has shown some effectiveness in addressing the widespread issue of unbounded activation growth across deep residual layers, it inevitably incurs significant communication overhead. To circumvent this bottleneck, we…
Barrett's algorithm is one of the most widely used methods for performing modular multiplication, a critical nonlinear operation in modern privacy computing techniques such as homomorphic encryption (HE) and zero-knowledge proofs (ZKP).…
This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…
In this paper, we develop a new Randomized Global Generalized Minimum Residual (RGlGMRES) algorithm for efficiently computing solutions to large scale linear systems with multiple right hand sides.The proposed method builds on a recently…
We present a novel, computationally simple method of hiding any message in the stream of random bits by using a secret key. The method is called Bury Among Random Numbers (BARN). A stream of random bits is produced by extracting the entropy…
Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…
Sparse general matrix multiplication (SpGEMM) is a fundamental building block for many real-world applications. Since SpGEMM is a well-known memory-bounded application with vast and irregular memory accesses, considering the memory access…
We revisit Fermat's factorization method for a positive integer $n$ that is a product of two primes $p$ and $q$. Such an integer is used as the modulus for both encryption and decryption operations of an RSA cryptosystem. The security of…
Difficulty of calculation of discrete logarithm for any arbitrary Field is the basis for security of several popular cryptographic solutions. Pohlig-Hellman method is a popular choice to calculate discrete logarithm in finite field $F_p^*$.…