Modular multiplication plays a crucial role in modern cryptography. Montgomery modular
multiplication (MMM), one of the most classic and practical modular multiplication …

In this paper, we presented a method of minimizing the number of overlapped partial
products in the accumulation of four-term Karatsuba multiplication. This method reduced the …

This paper presents an area-efficient Barrett Modular Multiplication (BMM) algorithm,
facilitating the development of cryptosystems like fully homomorphic encryption. Instead of …

Modular multiplication of long integers is a key component of elliptic curve cryptography and
homomorphic encryption. The multiplication complexity can be reduced by applying the …

Two algorithms, both based around multiplication, one defined by Andrew Donald Booth in
1950 and the other defined by Anatoly Alexeevitch Karatsuba in 1960 can be applied to …

The demand for efficient large integer polynomial multiplications in present day crypto-
systems is the need of the hour. Karatsuba-like multiplication is one of the most efficient …

The complexity of multipliers used to generate large random keys in cryptographic systems
contributes to the complexity of the entire cryptographic system, hence making it essential to …

This paper focusses on FPGA-based optimized implementations of asymmetrical three-term
Karatsuba multiplication (AThTKM) architecture. Two multiplications, AThTKM-I and AThTKM …

This work presents two methods of hardware implementation of area-time-product (ATP)-
optimized four-term Karatsuba multipliers (FTKM) on Field Programmable Gate Arrays …

This Paper proposed an enhanced Montgomery and efficient implementation of Modular
Multiplication. Cryptographyoprocess is usedufor providingphigh informationmsecurity when …