[curves] General Curve25519 and Ed25519 Libraries

[Michael Hamburg]

Hi Frank,

My library supports hashing to the curve, as do Snowshoe [*] and Libelligator [+], and not much else that I’m aware of.  Especially if you want it to be constant time and/or fast.  I’d bet that some of the other fancy libraries like PBC and MIRACL have it though.

I somehow misread your original message as “hashing points”.

Cheers,
— Mike

[*] https://github.com/catid/snowshoe <https://github.com/catid/snowshoe> by Christopher A Taylor

It’s pretty fast and uses a 254-bit field.  It doesn’t export point operations, but since it’s an Edwards curve it should be reasonably safe to use the internal APIs.

[+] https://github.com/Yawning/libelligator <https://github.com/Yawning/libelligator>

I found this by Googling.  It looks to be based on Donna.

> On Jun 18, 2015, at 11:01 AM, Frank Wang <frankw at mit.edu> wrote:
> 
> Hi Mike, 
> 
> Well, I want a way to translate a n-bit message to a point on the curve. My understanding is that it's easiest to hash it to the curve, but I could just be confused. 
> 
> Does your library not support hashing to the curve?
> 
> Frank
> 
> On Thu, Jun 18, 2015 at 1:50 PM, Mike Hamburg <mike at shiftleft.org <mailto:mike at shiftleft.org>> wrote:
> Wait, do you want to hash messages to the curve, or just be able to hash curve points?  The former is kind of a niche feature, though you could implement it yourself if the library doesn't support it. 
> 
> Sent from my phone.  Please excuse brevity and typos.
> 
> On Jun 18, 2015, at 10:38, Frank Wang <frankw at mit.edu <mailto:frankw at mit.edu>> wrote:
> 
>> Hi Thomas,
>> 
>> Yes. Sorry, my goal right now is that I have a key revocation scheme that I want to implement, involving elliptic curve addition, subtraction, and scalar multiplication (as well as hashing messages to the curve). I would like reasonable performance (so C does seem good) because I'm benchmarking it against AES. However, I'm willing to trade off some performance for ease of use.
>> 
>> TweetNacl seems to be designed primarily for ECDH and EC signatures rather than a general purpose elliptic curve library. I'm exploring alternatives.
>> 
>> Frank
>> 
>> On Thu, Jun 18, 2015 at 1:34 PM, Thomas DuBuisson <thomas.dubuisson at gmail.com <mailto:thomas.dubuisson at gmail.com>> wrote:
>> Frank,
>> A lot of recommendations are pouring in about C and Java libraries, on
>> top of which I'm tempted to recommend my own in Cryptol or one of the
>> Sage version out there, but none of us have heard about your actual
>> goal and needs.  Could you say more about how this code will be used
>> and what you hope to achieve?
>> 
>> Thomas
>> 
>> On Wed, Jun 17, 2015 at 2:16 PM, Frank Wang <frankw at mit.edu <mailto:frankw at mit.edu>> wrote:
>> > Hi,
>> >
>> > I am working on a research project at MIT, and I need to use elliptic curves
>> > (or a group where DDH is hard, but elliptic curves seem like the best way to
>> > go) to implement a cryptographic scheme. I've been trying to search for
>> > general Curve25519 and Ed25519 libraries where I can just do add and scalar
>> > multiply as well as hash messages to points. The best library I've come
>> > across so far is tweetnacl, which has the add and scalar multiply operation
>> > for Ed25519, but it's a bit difficult to use, and I end up modifying the
>> > library to do subtraction of points.
>> >
>> > I have yet to find a good library that allows me to just do operations on
>> > Ed25519 or Curve25519. Does such a library exist? If not, any tips on what I
>> > should do? Should I just use another curve library that is better supported?
>> > If so, any suggestions?
>> >
>> > Thanks,
>> > Frank
>> >
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