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Constant-time hardware implementation of Modular Inversion with Kaliski's Algorithm for ECC
Khai Nguyen1, Tung Nguyen1, Hung Nguyen1
1Integrated Circuits and Systems Laboratory, Ho Chi Minh City University of Technology (HCMUT), VNU-HCM, Ho Chi Minh City, Vietnam.
Abstract:
This paper introduces a hardware architecture designed for constant-time modular inversion over prime fields, a critical function in Elliptic Curve Cryptography (ECC). We use Kaliski's Almost Inversion Algorithm to develop an efficient FPGA-based solution. The proposed design guarantees constant-time execution, optimizing modular inverse computations for ECC applications. When synthesized on a Xilinx Kintex-7 FPGA, the accelerator reaches a frequency of 222.9 MHz, occupying 1.7k Slices without using any DSP blocks. This work focuses on improving the speed and resource usage of modular inversion units, specifically for resource-constrained digital environments.
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