A primer on elliptic curve cryptography

If you remember a bit of maths theory you know that you can define groups and things with multiplication and the like. It's that kind of idea.

The advantage is that the known best approaches to solving the DLP for integers don't carry across to the points on a curve (because the points don't work like integers for all of maths - they support enough to the crypto, but not enough for the attack). So you can use smaller keys.

AFAICT. IMHO. IANAM/C.

http://blog.rongarret.info/2013/02/a-simple-solution-to-cred...

You should never, ever, never, nevern, nervenvarn build your own production ECC code. ECC is particularly tricky to get right. But if you want to play with the concepts, a great place to start is the Explicit Formulas Database at http://www.hyperelliptic.org/EFD/ ; the fast routines for point multiplication are mercifully complicated, so copying them from the EFD is a fine way to start, instead of working them out from first principles.

He went on to say that only Adam Langley or Daniel Bernstein should be implementing ECC. Probably because there are so many ways to slip up; few others would have the experience necessary to avoid all the pitfalls.

'theboss agreed:

I've implemented ECC and you are 100% correct. Nobody should implement ECC unless you really really know what you're doing.

Mapping points to the curve, multiplying points, point addition, there is too much math stuff to mess up on. Just don't do it. If you read one thing tptacek says, read the last paragraph.

https://news.ycombinator.com/item?id=6607661

( Which I only still have open because I wanted to program the article at some point...)

Doing 2048 bit private rsa's for 10s: 1864 2048 bit private RSA's in 9.99s

That's 23 times as many signatures using ECDSA as RSA.

42 874 256

18 642 048

23 times as many signatures?