Journal of the Institute of Electronics Engineers of Korea CI (전자공학회논문지CI)

The Institute of Electronics and Information Engineers (대한전자공학회)
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An Implementation on the Computing Algorithm for Inverse Finite Field using Composite Field

합성체를 이용한 유한체의 역원 계산 알고리즘 구현

  • Noh Jin-Soo (Dept. of Electronic Engineering, Chosun University) ;
  • Rhee Kang-Hyeon (Dept. of Electronic Engineering, Chosun University)
  • Published : 2006.05.01
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Abstract

Recently, Finite field is applied the cryptography in the modern multimedia communication. Especially, block codes such as Elliptic Curve Cryptosystem and Reed-Solomon code among the error correcting codes are defined with finite field. Also, finite field algorithm is conducting the research actively because many kind of application parts need the real time operating ability therefore the exclusive hardware have been implementing. In this paper, we proposed the inverse finite field algorithm over GF($2^8$) using finite composite field and implemented in a hardware, and then compare this hardware with the currently used 'Itoh and Tsujii' hardware in respect to structure, area and computation time. Furthermore, this hardware was inserted into the AES SubBytes block and implemented on FPGA emulator board to confirm that the superiority of the proposed algorithm through the performance evaluation.

최근 멀티미디어 통신 시스템에서 유한체는 암호화 알고리즘에 적용되어지고 있으며. 특히 타원곡선 알고리즘 및 리드 솔로몬 등의 에러정정 코드는 유한체 상에서 정의 되어진다. 또한 많은 응용분야에서 유한체 연산의 실시간 처리를 요하므로 유한체 연산을 위한 전용 하드웨어 설계가 필요하게 되었고 이에 대한 많은 연구가 수행되어지고 있다. 본 논문에서는 합성체(Composite Field)를 이용하여 GF($2^8$)의 유한체의 역원을 계산할 수 있는 알고리즘을 제시하고 이를 하드웨어로 구현하여 현재 사용되어 있는 'Itoh and Tsujii' 하드웨어 구조와 면적 및 계산 속도의 성능을 비교 하였다. 또한 AES의 SubBytes 블록에 이를 삽입하여 FPGA 에뮬레이터 보드 상에서 구현하여 성능평가를 통하여 제시된 알고리즘의 우수성을 확인하였다.

Keywords

References

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