This brief introduces FPGA-based optimized implementation of Montgomery Modular
Multiplier (MMM) architecture. The novel architecture of the proposed design enhanced the …

Finite field multiplication is a fundamental and frequently used operation in various
cryptographic circuits and systems. Because of its high complexity, this operation generally …

Modular multiplication is a crucial operation in public-key cryptography systems such as
RSA and ECC. In this study, we analyze and improve the iteration steps of the classic …

In classical computation, Toom–Cook is one of the multiplication methods for large numbers
which offers faster execution time compared to other algorithms such as schoolbook and …

The proposed herein is a scalable high-radix (ie, 2 m) Montgomery Modular (MM)
Multiplication circuit replacing the integer multiplications in each iteration of the Montgomery …

The Montgomery modular multiplication is an integral operation unit in the public key
cryptographic algorithm system. Previous work achieved good performance at low input …

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 …

In this brief, Redundant Binary Representation (RBR) is applied in Montgomery modular
multiplication (MMM) to eliminate the long carry chain and realize parallel computation. A …

The extended GCD (XGCD) calculation, which computes Bézout coefficients ba, bb such
that ba∗ a0+ bb∗ b0= GCD (a0, b0), is a critical operation in many cryptographic …

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