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Efficient Implementation of Elliptic Curve Cryptography

Salarifard, Raziyeh | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51975 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Bayat-Sarmadi, Siavash
  7. Abstract:
  8. Elliptic curve cryptography (ECC) has received attention because it can achieve the same security level as other classical asymmetric methods while using a key with smaller length. Although ECC is more efficient compared to AlGemal and RSA cryptosystems, fast computation of ECC is always desirable. Point multiplication is an essential operation in cryptographic computations. Low-latency and low-complexity multiplication architectures lead to more efficient cryptosystems.In this thesis, a fixed-base comb point multiplication method has been used to perform regular point multiplication. Additionally, two low-complexity (LC) and low-latency (LL) architectures for the regular point multiplication using fixed-base comb method have been proposed.The point multiplication architectures have been implemented using field- programmable gate array (FPGA). The LC architecture implementation results over GF(2233), GF(2163), and GF(2283) show 62%, 46%, and 152% efficiency improvement, respectively. In addition, the LL architecture has 55%, 44%, and 76% reduction in point multiplication required time, respectively, over GF(2233), GF(2163), and GF(2283). Additionally, in this thesis, a high-throughput lowcomplexity unified field multiplier for triangular and dual bases is presented, and is referred to as basic architecture. Moreover, structurally improved architectures have been proposed, which have smaller time complexity than basic ones. This is achieved by the use of parallel processing method. Moreover, a low latency Karatsuba-Ofman based field multiplier (KOM) and an efficient point multiplication on Curve25519 have been proposed. The improvements have been achieved mainly due to the proposed low latency pipelined KOM and an efficient scheduling of
    field operations.s
  9. Keywords:
  10. Elliptic Curve Cryptography ; Fixed-Based Point Multiplication ; Field Multiplication ; High Efficiency Implementation

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