Earticle

초록

영어

Inversions in small finite fields are the most computationally intensive field arithmetic and have been playing a key role in areas of cryptography and engineering. The main algorithms for small finite field inversions are based on Fermat's little theorem, extended Euclidean algorithm, Itoh-Tsujii algorithm and other methods. In this brief, we present techniques to exploit special irreducible polynomials for fast inversions in small finite fields GF(2n) , where n is a positive integer and 0 < n < 16 . Then, we propose fast inversions based on Fermat's theorem for two special irreducible polynomials in small finite fields, i.e. trinomials and All-One-Polynomials (AOPs). Trinomials can be represented by polynomials xn + xm + 1 and AOPs can be represented by polynomials xn + Xn-1 + ... +1 , where m is a positive integer and 0 < m < n . Our designs have low hardware requirements, regular structures and are therefore suitable for hardware implementation. After that, our designs are programmed in Very-High-Speed Integrated Circuit Hardware Description Language (VHDL) by using integrated environment Altera Quartus II and implemented on a low-cost Field- Programmable Gate Array (FPGA). The experimental results on FPGAs show that our designs provide significant reductions in executing time of inversions in small finite fields, e.g. the executing time of inversion in GF(27) is 18.80 ns and the executing time of inversion in GF(212) is 29.57 ns.

목차

Abstract
 1. Introduction
 2. Preliminaries
  2.1. Finite Fields
  2.2. Inversions in Finite Fields
  2.3. FPGA
 3. Fast Inversions for Special Irreducible Polynomials in Small Finite Fields
  3.1. Fast Inversions Based on Fermat's Theorem
  3.2. Fast Inversions for Trinomials Xn + x + 1
  3.3. Fast Inversions for AOPs
 4. Implementation
 5. Conclusion
 Acknowledgments
 References

키워드

저자

• Haibo Yi [ School of Computer Engineering, Shenzhen Polytechnic. 518055 Shenzhen, China ]
• Weijian Li [ School of Computer Science, Guangdong Polytechnic Normal University. 510000 Guangzhou, China ]
• Zhe Nie [ School of Computer Engineering, Shenzhen Polytechnic. 518055 Shenzhen, China ]

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Security and Its Applications

• 간기

  격월간

• pISSN

  1738-9976

• 수록기간

  2008~2016

• 등재여부

  SCOPUS

• 십진분류

  KDC 505 DDC 605