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Elliptic Curve Key Agreement Schemes

  • Reference work entry
Encyclopedia of Cryptography and Security

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Related Concepts

Diffie–Hellman Key Agreement; Elliptic Curve Cryptography; Key Agreement

Definition

Key agreement schemes establish a shared secret between two or more parties. The versions described here are variants of Diffie–Hellman key agreement schemes.

Background

Classic Diffie–Hellman is an unauthenticated protocol to establish a shared secret. For a discussion of attacks and authentication, Diffie–Hellman Key Agreement.

Applications

In the elliptic curve analogue of the basic Diffie-Hellman key agreement scheme [4], two users A and B share domain parameters \(D = (q,\mbox{ FR},S,a,b,P,n,h)\) (Elliptic Curve Keys). A selects an integer \({d}_{A} {\in }_{R}[1,n - 1]\) and sends Q A = d A P to B. Similarly, B selects an integer \({d}_{B} {\in }_{R}[1,n - 1]\) and sends Q B = d B P to A. A computes \(K = {d}_{A}{Q}_{B} = {d}_{A}{d}_{B}P\), and B similarly computes K = d B Q A . The shared secret point Kis used to derive a secret key that can then be used to encrypt or...

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Recommended Reading

  1. ANSI X9.63 (2001) Public key cryptography for the financial services industry: key agreement and key transport using elliptic curve cryptography. American National Standards Institute, Washington, DC

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  6. IEEE Std 1363-2000 (2000) IEEE standard specifications for public-key cryptography

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  7. ISO/IEC 15946-3 (2002) Information technology – security techniques – cryptographic techniques based on elliptic curves – Part 3: key establishment

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  9. SP 800-56A (2007) Special publication 800-56A, Recommendation for pair-wise key establishment schemes using discrete logarithm cryptography. National Institute of Standards and Technology US Gaithersburg, Maryland

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Author information

Authors and Affiliations

  1. Department of Mathematics, Auburn University, 221 Parker Hall, 36849-5307, Auburn, AL, USA

    Darrel Hankerson

  2. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alfred Menezes

Authors
  1. Darrel Hankerson
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  2. Alfred Menezes
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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© 2011 Springer Science+Business Media, LLC

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Hankerson, D., Menezes, A. (2011). Elliptic Curve Key Agreement Schemes. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_247

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