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Generation and Implementation of Cryptographically Strong Elliptic Curves

Part of the Lecture Notes in Computer Science book series (LNSC,volume 10737)

Abstract

Elliptic curves over finite fields are an essential part of public key cryptography. The security of cryptosystems with elliptic curves is based on the computational intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). The paper presents requirements which cryptographically secure elliptic curves have to satisfy, together with their justification and some relevant examples of elliptic curves. We implemented modular arithmetic in a finite field, the operations on an elliptic curve and the basic cryptographic protocols.

Keywords

  • Elliptic curve cryptography
  • Modular arithmetic
  • Digital signature ECDSA
  • Diffie-Hellman key agreement

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Correspondence to Janusz Szmidt .

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Appendix: The Examples of Elliptic Curves

Appendix: The Examples of Elliptic Curves

Table 6. Domain parameters for a 160-bit elliptic curve
Table 7. Domain parameters for a 256-bit elliptic curve
Table 8. Domain parameters for a 384-bit elliptic curve
Table 9. Domain parameters for a 512-bit elliptic curve

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Dąbrowski, P., Gliwa, R., Szmidt, J., Wicik, R. (2018). Generation and Implementation of Cryptographically Strong Elliptic Curves. In: Kaczorowski, J., Pieprzyk, J., Pomykała, J. (eds) Number-Theoretic Methods in Cryptology. NuTMiC 2017. Lecture Notes in Computer Science(), vol 10737. Springer, Cham. https://doi.org/10.1007/978-3-319-76620-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-76620-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-76619-5

  • Online ISBN: 978-3-319-76620-1

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