This MATLAB function efficiently computes the inverse of a square matrix using LU factorization. By decomposing the matrix into lower and upper triangular matrices, the function solves for the inverse ...

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Abstract: The Lenstra's elliptic curve factorization (LEF) algorithm is a problem to factor a composite number N that is a modulus to define an elliptic curve over it, namely E mod N. The LEF method ...

RSA cryptography, which is one of the typical public key cryptosystems, is a cryptosystem based on the fact that it is difficult to factor a composite number with a large number of digits into prime ...

Abstract: The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process.

We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the ...

We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor’s algorithm. We implement the algorithm in a NMR quantum information processor and experimentally ...