Curve25519 is a pretty secure way to exchange a key. In the original Paper and on SafeCurves a lot of attacks and security aspects are mentioned:


  • Brute force: This one is theoretically possible but not practical
  • Small subgroup attacks: Pohlig Hellman and Lim Lee attacks are useless against Curve25519 mostly because of the chosen parameters.
  • Pollard Rho and Kangaroo attacks: Curve25519 is not immune to those attacks, but still provides enough security ( round about $2^{125}$ )
  • Batch discrete logarithms: Again Curve25519 is not immune but still provides enough security
  • Transfer attacks: Algebraic attack against which Curve25519 is pretty much resistant
  • Baby Step Giant Step: Is possible but the cyclic groups are too big.

Other security aspects:

  • Rigidity: The origin for every Curve25519 parameter is provided
  • Montgomery Ladder: Resistance against side channel attack
  • Twist: The Twist of Curve25519 is secure, too
  • Completeness: addition formula is complete
  • Indistinguishability: No difference between a random string and a key

Since Curve25519 was published about 15 years ago my question is: Are there any (newer) attacks and/or security aspects I'm missing?

  • $\begingroup$ I already saw that, but my main questions is: Are there any new attacks since then? $\endgroup$
    – Titanlord
    Jul 17, 2020 at 8:59
  • 1
    $\begingroup$ Here's a side-channel attack using the points of order 4: eprint.iacr.org/2017/806 $\endgroup$
    – Sam Jaques
    Jul 17, 2020 at 9:03
  • $\begingroup$ @Titanlord To be a good question, most of the people here, want to see where you get the results. This can be achieved by providing the links that contributes to your question/knowledge. $\endgroup$
    – kelalaka
    Jul 17, 2020 at 9:20
  • $\begingroup$ Uhm... My sources where the Curve25519 paper and the SafeCurve Website. Both are linked. $\endgroup$
    – Titanlord
    Jul 17, 2020 at 9:26


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