정보보호학회논문지 (Journal of the Korea Institute of Information Security & Cryptology)

  • 제9권4호
  • /
  • Pages.3-10
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  • 1999
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  • 1598-3986(pISSN)
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  • 2288-2715(eISSN)
한국정보보호학회 (Korea Institute of Information Security and Cryptology)
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변형된 다항식 기저를 이용한 유한체의 연산

Arithmetic of finite fields with shifted polynomial basis

  • 발행 : 1999.12.01
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⟨ 이전 논문 다음 논문 ⟩

초록

유한체(Galois fields)가 타원곡선 암호법 coding 이론 등에 응용되면서 유한체의 연 산은 더많은 관심의 대상이 되고 있다. 유한체의 연산은 표현방법에 많은 영향을 받는다. 즉 최적 정규기 저는 하드웨 어 구현에 용이하고 Trinomial을 이용한 다항식 기저는 소프트웨어 구현에 효과적이다. 이논문에서는 새로운 변형된 다항식 기저를 소개하고 AOP를 이용한 경우 하드웨어 구현에 효과적인 최 적 정규기저와 의 변환이 위치 변화로 이루어지고 또한 이것을 바탕으로 한 유한체의 연산이 소프트웨어적 으로 효율적 임을 보인다. More concerns are concentrated in finite fields arithmetic as finite fields being applied for Elliptic curve cryptosystem coding theory and etc. Finite fields arithmetic is affected in represen -tation of those. Optimal normal basis is effective in hardware implementation and polynomial field which is effective in the basis conversion with optimal normal basis and show that the arithmetic of finite field with the basis is effective in software implementation.

More concerns are concentrated in finite fields arithmetic as finite fields being applied for Elliptic curve cryptosystem coding theory and etc. Finite fields arithmetic is affected in represen -tation of those. Optimal normal basis is effective in hardware implementation and polynomial field which is effective in the basis conversion with optimal normal basis and show that the arithmetic of finite field with the basis is effective in software implementation.

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참고문헌

  1. Crypto'98 Optimal extension field for fast arithmetic in public key algorithm D.V. Baily;C. Paar
  2. Crypto'97 Efficient algorithms for elliptic curve cryptosystems J. Guajardo;C. Paar
  3. Eurocrypt'92 Public-Key Cryptosystems with very small Key length G. Harper;A. Menezes;S.A. Vanstone
  4. IEEE Transactions on Computers v.42 no.10 A modified Massey-Omura Parallel multiplier for a class of finite fields M.A. Hasan;M.Z. Wang;V.K. Bhargava
  5. J. Society for Electronic Communications v.44 A fast algorithm for computing multiplicative inverses in GF($2_t$) using normal bases T. Itoh;O. Teechai;S. Tsuji
  6. SAC'98 Storage-Efficient Finite Field Basis Conversion B.S. Kaliski Jr;Y.L. Yin
  7. Mathematics of Computation v.48 Elliptic curve crypto-systems N. Koblitz
  8. IEEE Transactions on Computers v.47 no.3 Low complexity bit-parallel canonical and normal basis multiplier for a class of finite fields C.K. Koc;B. Sunar
  9. Introduction to finite fields and their applications R. Lidl;H. Niederreiter
  10. Applications of finite fields A.J. Menezes
  11. Crypto'85 Use of elliptic curve in cryptography V. S. Miller
  12. Crypto 95 Fast key exchange with elliptic curve systems R. Schroeppel;H. Orman;S. O'Malley;O. Spatscheck
  13. Asiacrypt 96 A fast software implementation for arithmetic operations in GF($2^t$) E. De Win;A. Bosselaers;S. Vandenberghe;P. De Gersem;J. Vandewalle
  14. IEEE P1363 Standard specification for public key cryptography