대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제18권1호
  • /
  • Pages.159-168
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  • 2003
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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IMPLEMENTATION ISSUES FOR ARITHMETIC OVER EXTENSION FIELDS OF CHARACTERISTIC ODD

  • Oh, Sang-Ho (Center for Information Security Technologies Korea University) ;
  • Kim, Chang-Han (Department of Information Security Semyung University) ;
  • Kim, Yong-Tae (Department of Mathematcs Education Kwangju National University of Education) ;
  • Park, Young-Ho (Department of Information Security and Systems Sejong Cyber University)
  • 발행 : 2003.01.01
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초록

In this paper we discuss the Construction Of 3 new extension field of characteristic odd and analyze the complexity of arithmetic operations over such a field. Also we show that it is suitable for Elliptic Curve Cryptosystems(ECC) and Digital Signature Algorithm(DSA, 〔7〕) as an underlying field. In particular, our digital signature scheme is at least twice as efficient as DSA.

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참고문헌

  1. Mathematics of Computation v.61 A subexponential algorithm for discrete logarithms over all finite fields L. M. Adleman;Jonathan DeMarrais https://doi.org/10.2307/2152932
  2. Crypto'98, LNCS 1462 Optimal extension fields for fast arithmetic in public-key algorithms D. V. Bailey;Christof Paar
  3. Conference on The Mathematics of Public Key Cryptography Inversion in Optional Extension Fields D. V. Bailey;Christof Paar
  4. Asiacrypt '96, LNCS 1163 A fast software implementation for arithmetic operations in $GF(2^{t})$ E. De Win;A. Bosselaers;S. Vandenberghe;P. De Gersem;J. Vandewalle
  5. IEEE Trans. Computers v.51 no.1 A new Hardware architecture for operations in $GF(2^{m})$ C. H. Kim;S. Oh;J. Lim https://doi.org/10.1109/12.980019
  6. Eurocrypt '96 New modular multiplication algorithms for fast modular exponentiation S. M. Hong;S. Y. Oh;H. S. Yoon
  7. Handbook of applied cryptography A. J. Menezes;P. C. van Oorschot;S. A. Vanstone
  8. Applications of finite fields A. J. Menezes
  9. Mathematics of Computation v.44 Modular multiplication without trial division P. L. Montgomery https://doi.org/10.2307/2007970
  10. Contribution to IEEE P1363 Proposing the use of non-conventional basis of finite fields S. Oh;C. H. Kim
  11. Information and Computation v.78 A fast algorithm for computing multiplicative inverses in $GF(2^{m})$ using normal bases T. Itoh;S. Tsujii https://doi.org/10.1016/0890-5401(88)90024-7