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Elliptic Curve Public-Key Encryption Schemes

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Encyclopedia of Cryptography and Security

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Related Concepts

ElGamal Public Key Encryption; Elliptic Curve Cryptography

Definition

Elliptic curve public-key encryption schemes rely on the properties of elliptic curves for public-key encryption and decryption. An elliptic curve analogue of ElGamal public-key encryption is described.

Background

It is possible to develop elliptic curve analogues of all the variants of the ElGamal public-key encryption scheme [3]. Described here is one such variant, the Elliptic Curve Integrated Encryption Scheme (ECIES), proposed by Abdalla, Bellare, and Rogaway [1].

Applications

In ECIES, the elliptic curve domain parameters are \(D = (q,\mbox{ FR},S,a,b,P,n,h)\), and an entity A’s key pair is (d, Q) (Elliptic Curve Keys). Edenotes a symmetric-key encryption scheme such as the AdvancedEncryption Standard (AES), and Message Authentication Code (MAC)denotes a message authentication code algorithm such as HashedMessage Authentication Code (HMAC). In order to encrypt a messagem toA, anentity Bdoes...

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Recommended Reading

  1. Abdalla M, Bellare M, Rogaway P (2001) The oracle Diffie–Hellman assumptions and an analysis of DHIES. Topics in cryptology—CT-RSA 2001, Lecture Notes in Computer Science, vol 2020. Springer, Berlin, pp 143–158

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  2. Cramer R, Shoup V (1998) A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. Advances in cryptology—CRYPTO ’98, Lecture Notes in Computer Science, vol 1462. Springer, Berlin, pp 13–25

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  3. 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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  4. ISO/IEC 18033-2 (2006) Information Technology – Security Techniques – Encryption algorithms – Part 2: asymmetric ciphers

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  5. Rackoff C, Simon D (1992) Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. Advances in Cryptology—CRYPTO ’91, Lecture Notes in Computer Science, vol 576. Springer, pp 433–444

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  6. Shoup V (ed) (2004) FCD 18033-2 Encryption algorithms Part 2: asymmetric ciphers. http://www.shoup.net/iso

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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 Public-Key Encryption 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_250

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