.png){kind=icon}
.png){kind=icon}
Return
Division-Free Four-Way Toom-Cook Polynomial Multiplication Architecture for Large Integer Arithmetic on FPGAs and ASICs
.png){kind=icon}
PRE
AI
M
B
DOI：10.1109/TCAD.2025.3608645.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Polynomial multiplication performs as the most important task and is computationally extensive in cryptographic algorithms. Of the several polynomial multiplications, theoretically, the Toom-Cook multiplication is the most efficient. In this article, an efficient four-way Toom-Cook (Toom-4) multiplication method has been presented that provides accurate result as the product and can be efficiently implemented in hardware. This is done by eliminating the effects of exact divisions present in the intermediate steps of the computation. In addition to these, the hardware implementation of the proposed work suggests that this multiplication method performs better in terms of resource utilization and delay minimization compared with other existing Toom-4 algorithm methods. Hardware implementation of the proposed Toom-4 multiplication architecture is done using a Virtex-7 FPGA device in Xilinx (now AMD) ISE platform. Here, the hardware implementation of the proposed multiplier is performed for 128, 256, and 512 bits with advantages in the area-time-product (ATP) over previous researches; ATP is the figure of merit in determining the performance of the design. Practically for 512 input bits, the percentage ATP of the proposed design is 98.810%, 23.537% and 57.316% better compared with Toom-2 (Karatsuba) multiplication, hybrid Toom-2 (Karatsuba-Comba) multiplication, and existing Toom-4 multiplication, respectively. Moreover, application-specific integrated circuit (ASIC) implementation results on United Microelectronics Corporation (UMC) 65-nm technology demonstrate a notable reduction in ATP and power-time-product (PTP) compared with state-of-the-art works.
Keywords:
Polynomials
Hardware
Field programmable gate arrays
Cryptography
Elliptic curve cryptography
Computer architecture
Accuracy
Interpolation
Resource management
Program processors
Application-specificintegrated circuits (ASICs)
field-programmable gate arrays (FPGAs)
four-way Toom-Cook (Toom-4) multiplication
polynomial multiplication
post-quantum cryptography (PQC)
schoolbook multiplication
Journal
I
IF:
2.9
Papers:
564
Citations:
9.6K
Organization
No organization information available
Cited Papers