Constant-time hardware implementation of Modular Inversion with Kaliski's Algorithm for ECC

Area of Science:

• Computer Engineering
• Cryptography
• Hardware Acceleration

Background:

• Modular inversion is a key operation in Elliptic Curve Cryptography (ECC).
• Existing methods can be time-consuming and resource-intensive, especially in constrained environments.
• Constant-time execution is vital for security in cryptographic applications.

Purpose of the Study:

• To introduce a novel hardware architecture for constant-time modular inversion over prime fields.
• To optimize modular inverse computations for Elliptic Curve Cryptography (ECC) applications.
• To improve the speed and resource utilization of modular inversion units.

Main Methods:

• Utilized Kaliski's Almost Inversion Algorithm for efficient computation.
• Developed a Field-Programmable Gate Array (FPGA)-based hardware solution.
• Designed for guaranteed constant-time execution.

Main Results:

• Achieved a frequency of 222.9 MHz when synthesized on a Xilinx Kintex-7 FPGA.
• The design occupies 1.7k Slices, without utilizing any Digital Signal Processing (DSP) blocks.
• Demonstrated efficient modular inverse computations for ECC.

Conclusions:

• The proposed hardware architecture offers a high-speed, resource-efficient solution for constant-time modular inversion.
• This work is particularly beneficial for resource-constrained digital systems implementing ECC.
• The design contributes to enhancing the performance and security of cryptographic hardware.