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High-Performance Architecture for Post-Quantum Cryptography Based on Elliptic Curve Isogeny

Farzam, Mohammad Hossein | 2021

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 55305 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Bayat Sarmadi, Siavash
  7. Abstract:
  8. Public-key cryptography is vital to secure digital communication. The classic instances of these cryptosystems are insecure against large-scale quantum computers. As a result, post-quantum cryptography has emerged as a replacement, which includes different categories. Isogeny-based schemes are one of the promising candidates mainly because of their smaller public key length. Due to high computational cost of such schemes, efficient implementations are significantly important. In this thesis, we have presented various solutions at three different abstraction layers. At the lowest layer, which deals with modular arithmetic, two hardware architectures are presented to perform modular multiplication faster as well as a faster way of performing modular inversion. At the second layer, which deals with a sequence of modular operations, i.e., the subroutines, we have provided an efficient scheduling powered by constraint programming. At the highest layer, which deals with a sequence of subroutines, we present a dynamic algorithm which helps change the sequence to reach a more parallelizable and faster computation strategy for isogenies with large but smooth degrees. As a practical evaluation, we have implemented the supersingular isogeny key encapsulation (SIKE) mechanism on a Virtex-7 FPGA at four different security levels. Experimental results show that, by employing these optimizations, this cryptosystem can be performed at least 1.79 times faster than the state-of-the-art while improving the area-time product metric by at least 1.35 times.
  9. Keywords:
  10. Isogeny-based Cryptography ; Parallel Processing ; Post-Quantum Cryptography ; Modular Multiplier ; Task Scheduling Algorithm ; Field Programmable Gate Array (FPGA) ; Diffie-Hellman Problem ; Modular Inversion ; Supersingular Isogeny Diffie-Hellman (SIDH) ; Supersingular Isogeny Key Encapsulation (SIKE) ; Montgomery Multiplication

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