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Elliptic Curve Signature Schemes

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Encyclopedia of Cryptography and Security

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Related Concepts

Digital Signature Schemes; Elliptic Curve Cryptography

Definition

Elliptic curve signature schemes rely on properties of elliptic curves for signature generation and verification. The Elliptic Curve Digital Signature Algorithm (ECDSA) variant is described, an analogue of the Digital Signature Algorithm (DSA).

Background

Many variants of the ElGamal digital signature scheme [1] have been proposed including the DSA [2], Schnorr’s signature scheme [8], the Nyberg–Rueppel signature scheme [6], and the Korean certificate-based digital signature algorithm (KCDSA) [5]. Some of these variants have been proven to be existentially unforgeable by adaptive chosen-message attacks [3] under certain assumptions including intractability of the elliptic curve discrete logarithm problem (ECDLP) (see [7]). ECDSA, an elliptic curve analogue of the DSA, is outlined here; for further details, see [ 4].

Applications

In ECDSA, the elliptic curve domain parameters are \(D = (q,\mbox{...

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Recommended Reading

  1. ElGamal T (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inf Theory 31:469–472

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  2. FIPS 186-3 (2009) Digital signature standard (DSS), Federal Information Processing Standards Publication 186-3, National Institute of Standards and Technology, Gaithersburg, Maryland

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  3. Goldwasser S, Micali S, Rivest R (1988) A digital signature scheme secure against adaptive chosen-message attacks. SIAM J Comput 17:281–308

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  4. Johnson D, Menezes A, Vanstone S (2001) The elliptic curve digital signature algorithm (ECDSA). Internat J Inf Security 1:36–63

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  5. Lim C, Lee P (1998) A study on the proposed Korean digital signature algorithm. Advances in Cryptology—ASIACRYPT ’98, Lecture Notes in Computer Science, vol 1514. Springer, pp 175–186

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  6. Nyberg K, Rueppel R (1996) Message recovery for signature schemes based on the discrete logarithm problem. Design Codes Cryptogr 7:61–81

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  7. Pointcheval D, Stern J (2000) Security arguments for digital signatures and blind signatures. J Cryptol 13:361–396

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  8. Schnorr C (1991) Efficient signature generation by smart cards. J Cryptol 4:161–174

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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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Hankerson, D., Menezes, A. (2011). Elliptic Curve Signature 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_251

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