Algorithms for polynomial computation over finite fields form a crucial domain in computational mathematics, with extensive applications ranging from cryptography and ...

In this project, Karatsuba algorithm for polynomial multiplication is synthesized and simulated in Xilinx Vivado 2019.2 using verilog HDL. Folders and Files info: KA_2bit: KA_2bit.v KA_4bit: KA_2bit.v ...

Multiplication is an essential step in a lot of calculations. In this paper we look at multiplication of 2 binary polynomials of degree at most n − 1, modulo an irreducible polynomial of degree n with ...

Abstract: Representing the field elements with respect to the polynomial (or standard) basis, we consider bit parallel architectures for multiplication over the finite field GF(2m). In this effect, ...

Abstract: Quantum computers pose a significant threat to modern cryptographic systems by efficiently solving problems such as integer factorization through Shor’s algorithm. Homomorphic encryption (HE ...

Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of ...

Polynomial Class in Python: A Python implementation of a Polynomial class that supports addition, subtraction, multiplication by a number, evaluation for specific values, and a human-readable string ...

ABSTRACT: Substitution boxes or S-boxes play a significant role in encryption and de-cryption of bit level plaintext and cipher-text respectively. Irreducible Poly-nomials (IPs) have been used to ...