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A practical implementation of elliptic curve cryptosystems over GF(p) on a 16-bit microcomputer

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Public Key Cryptography (PKC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1431))

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Abstract

Recently the study and implementation of elliptic curve cryptosystems (ECC) have developed rapidly and its achievements have become a center of attraction. ECC has the advantage of high-speed processing in software even on restricted environments such as smart cards. In this paper, we concentrate on implementation of ECC over a field of prime characteristic on a 16-bit microcomputer M16C (10MHz). We report a practical software implementation of a cryptographic library which supports 160-bit elliptic curve DSA (ECDSA) signature generation, verification and SHA-1 on the processor. This library also includes general integer arithmetic routines for applicability to other cryptographic algorithms. We successfully implemented the library in 4Kbyte code/data size including SHA-1, and confirmed a speed of 150msec for generating an ECDSA signature and 630msec for verifying an ECDSA signature on M16C.

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References

  1. N.Koblitz, ”Elliptic curve cryptosystems”, Mathematics of Computation, 48(1987),203–209.

    Article  MATH  MathSciNet  Google Scholar 

  2. V.S.Miller, ”Use of elliptic curves in cryptography”, Advances in Cryptology-Proceedings of Crypto'85, Lecture Notes in Computer Science, 218(1986), Springer-Verlag, 417–426.

    Google Scholar 

  3. G. Agnew, R. Mullin and S. Vanston, ”An Implementation of elliptic curve cryptosystems over \(F_{2^{155} }\)”, IEEE Journal on Selected Areas in Communications,11(1993),804–813.

    Article  Google Scholar 

  4. Certicom SigGen Smart Card, http://205.150.149.57/ce2/embed.htm.

    Google Scholar 

  5. T.ElGamal, ”A public key cryptosystem and a signature scheme based on discrete logarithm”, IEEE Trans. Inform. Theory, Vol.IT-31(1985),469–472.

    Article  MathSciNet  Google Scholar 

  6. IEEE P1363 Working Draft Appendices, February 6, 1997.

    Google Scholar 

  7. IEEE P1363 Draft Version 1, December 19, 1997.

    Google Scholar 

  8. G. Harper, A.Menezes and S.Vanstone, ”Public-key cryptosystems with very small key lengths”, Advances in Cryptology-Proceedings of Eurocrypt'92, Lecture Notes in Computer Science, 658(1993), Springer-Verlag, 163–173.

    Google Scholar 

  9. R. Schroeppel, H. Orman, S. O'Malley and O. Spatscheck, ”Fast key exchange with elliptic curve systems”, Advances in Cryptology-Proceedings of Crypt'95, Lecture Notes in Computer Science, 963(1995), Springer-Verlag, 43–56.

    Google Scholar 

  10. E.D.Win, A.Bosselaers and S.Vandenberghe, ”A fast software implementation for arithmetic operations in GF(2n)”, Advances in Cryptology-Proceedings of Asiacrypt'95, Lecture Notes in Computer Science, 1163(1996), Springer-Verlag, 65–76.

    Google Scholar 

  11. A.Miyaji, T.Ono and H.Cohen, ”Efficient Elliptic Curve Exponentiation”, Information and Communications Security ICICS'97, Lecture Notes in Computer Science,1334(1997), Springer-Verlag, 282–291.

    Google Scholar 

  12. ”User Manual of M16C/60 Series”, Mitsubishi Electric Corporation, 1996.

    Google Scholar 

  13. ”Software Manual of M16C/60 Series”, Mitsubishi Electric Corporation, 1996.

    Google Scholar 

  14. National Institute of Standards and Technology, NIST FIPS PUB 186, ”Digital Signature Standard”, U.S. Department of Commerce, 1994.

    Google Scholar 

  15. National Institute of Standards and Technology, NIST FIPS PUB 180, ”Secure Hash Standard”, U.S. Department of Commerce, 1995.

    Google Scholar 

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Hideki Imai Yuliang Zheng

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© 1998 Springer-Verlag Berlin Heidelberg

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Hasegawa, T., Nakajima, J., Matsui, M. (1998). A practical implementation of elliptic curve cryptosystems over GF(p) on a 16-bit microcomputer. In: Imai, H., Zheng, Y. (eds) Public Key Cryptography. PKC 1998. Lecture Notes in Computer Science, vol 1431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054024

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  • DOI: https://doi.org/10.1007/BFb0054024

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64693-8

  • Online ISBN: 978-3-540-69105-1

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