Nature

Optimized quantum folding Barrett reduction for quantum modular multipliers

Quantum computers can solve numerous problems faster, based on quantum properties such as superposition and entanglement, than classical computers. For example, Shor’s algorithm 1, proposed by Peter ...
IEEE

Area and Delay Trade-Offs in Three-Way Toom-Cook Large Integer Multipliers Implemented on FPGAs

Abstract: The demand for efficient large integer polynomial multiplications in present day crypto-systems is the need of the hour. Toom-Cook multiplication algorithm being one of the most efficient ...
IEEE

Efficient Barrett Modular Multiplication Based on Toom-Cook Multiplication

Abstract: The Toom-Cook multiplier (TCM) is the most suitable method for multiplying large integers with key widths typically employed in ECC or RSA due to its computational efficiency. In this brief, ...
Scientific Research Publishing

A. Toom, “The Complexity of a Scheme of Functional Elements Realizing the Multiplication of Integers,” Soviet Mathematics-Doklady, Vol. 7, 1963, pp. 714-716.

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

A. Karatsuba and Yu. Ofman, “Multiplication of Multidigit Numbers on Automata,” Soviet Physics-Doklady, Vol. 7, 1963, pp. 595-596.

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