USE: It is used for modular exponentiation for large value of exponent i.e. for calculating [(a ^ b) % m] for some a, b & m . COMPLEXITY: The running time of this algorithm is O(log exponent). This ...

This project demonstrates the concept of Matrix Exponentiation and its application in solving problems efficiently. Specifically, it illustrates how matrix exponentiation can be used to calculate the ...

Abstract: Modular exponentiation with a large modulus, which is usually accomplished by repeated modular multiplications, has been widely used in public key cryptosystems for secured data ...

Montgomery algorithms represent a transformative advancement in the computation of modular arithmetic, specifically designed to bypass the costly division steps inherent in traditional methods. By ...

The content of this paper is a detailed analysis of possible ways how to quantum implement a key part of Shor’s factorization algorithm, the modular exponentiation function. This implementation is a ...

Abstract: Modular exponentiation, an operation widely utilized in cryptographic protocols to transfer text and other forms of data, can also be applied to Internet-of-Things (IoT) devices with high ...