Top 10 papers in ECC

Mara wrote the comment “I don’t want to start by books on ECC, I want to read papers”. A short reply is: go to and read the most recent papers which mention elliptic curves.

But the question got me thinking: What are the 10 most “influential” papers in elliptic curve cryptography. What are the papers that everyone in the subject should have read? I thought it might be interesting to compile such a list.

Quickly my list fell into two lists:

  • papers actually about elliptic curves and cryptography and implementation;
  • papers about the elliptic curve discrete logarithm problem and related computational assumptions (for example, the famous MOV and Frey-Rueck papers).

So I am restricting my attention to the first list. Maybe I’ll do a top 10 about ECDLP another time.

Below is my list of the 10 most influential papers that everyone should read. The reader should understand that these papers are usually the starting point of whole sub-areas; hence there are many subsequent papers which generalise/extend/improve the results in these papers. To become expert in ECC it is necessary to also read the papers which follow-on from the ones in the below list.

  1. V. S. Miller, Use of elliptic curves in cryptography, CRYPTO 1985.

    This paper, together with the next one, started the whole subject. It is fascinating to read them together, as they have almost entirely disjoint contents.

  2. N. Koblitz, Elliptic curve cryptosystems, Math. Comp., Vol. 48, 1987.
  3. C.-P. Schnorr, Efficient Identification and Signatures for Smart Cards, CRYPTO 1989.

    Introduced Schnorr signatures, which are the best digital signature scheme for elliptic curves (even though ECDSA is more widely promoted).

  4. J. Solinas, Efficient arithmetic on Koblitz curves, Des. Codes Crypt., Vol. 19, 2000.

    Gives a beautiful analysis of Frobenius expansions.

  5. R. P. Gallant, R. J. Lambert and S. A. Vanstone, Faster point multiplication on elliptic curves with efficient endomorphisms, CRYPTO 2001.

    Introduced an excellent method for fast ECC.

  6. M. Abdalla, M. Bellare and P. Rogaway, DHIES: An encryption scheme based on the Diffie-Hellman Problem.

    This unpublished paper tells the right way to encrypt using elliptic curves.

  7. R. Cramer and V. Shoup, Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack, SIAM J. Comput., Vol. 33, 2003.

    This is the journal version of their CRYPTO 1998 paper. The first encryption scheme based on DLP secure in the standard model.

  8. D. Boneh and M. K. Franklin, Identity based encryption from the Weil pairing, SIAM J. Comput., Vol. 32, 2003.

    Journal version of the paper that really kick-started pairing-based cryptography.

  9. D. Boneh, B. Lynn and H. Shacham, Short signatures from the Weil pairing, ASIACRYPT 2001 or Journal of Cryptology, Vol. 17, 2004.

    Another paper which showed early applications of pairing-based cryptography.

  10. D. J. Bernstein and T. Lange, Faster addition and doubling on elliptic curves, ASIACRYPT 2007.

    The paper that first showed that Edwards curves might have some advantages for ECC.

Many of you will think I have missed out something important. If so, then leave a comment.

— Steven Galbraith

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One Response to Top 10 papers in ECC

  1. Mara says:

    Thank you very much, I will start collecting them and reading them.

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