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Hwajeong Seo1, Hyunjin Kim, Taehwan Park

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Summary

This study introduces a novel pre-computation method for elliptic curve cryptography (ECC) scalar multiplication. The new approach enhances efficiency on resource-constrained devices by optimizing pre-computation tables for embedded microprocessors.

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Area of Science:

  • Cryptography and Information Security
  • Computer Engineering and Embedded Systems

Background:

  • Elliptic Curve Cryptography (ECC) is a leading public-key technique due to its short key sizes and versatile crypto protocols.
  • Implementing ECC on resource-constrained devices requires optimizing computationally intensive operations like scalar multiplication.
  • Existing methods utilize Non-Adjacent Form (NAF) and width-w NAF representations with modified pre-computation tables.

Purpose of the Study:

  • To propose a new pre-computation method for ECC scalar multiplication that increases zero occurrences.
  • To enhance the speed performance of ECC on resource-constrained devices.
  • To develop a customizable pre-computation table for embedded microprocessors.

Main Methods:

  • Developed a novel pre-computation method for scalar multiplication with a higher frequency of zero occurrences.
  • Combined the proposed method with existing techniques to manage pre-computation table size for practical applications.
  • Introduced a structure allowing fine-tuning of speed performance and table size.

Main Results:

  • The new pre-computation method significantly increases zero occurrences compared to previous approaches.
  • The combined method offers a practical solution for implementing ECC on embedded systems.
  • A customized look-up table for embedded microprocessors was established, balancing performance and memory usage.

Conclusions:

  • The proposed pre-computation method effectively optimizes ECC scalar multiplication for resource-constrained environments.
  • The ability to customize pre-computation tables allows for tailored performance on embedded microprocessors.
  • This research contributes to more efficient and practical ECC implementations in embedded systems.