Elliptic curve cryptography (ECC)

[ragdog]

Hi

I serach a while on net for an example about Elliptic curve cryptography (ECC)
have any an example about it?

Thanks

[bozo]

I don't know enough about it but are you just looking for assembly implementations? i'm assuming that's what you want.
there aren't any open source assembly libraries that i know of except for one WiteG did 5 years ago.

ECC is quite complicated to implement and can't really be shown in small example  :bg

MrHaandi has assembly code for ECC operations and probably others have too but unfortunately not open source...
WiteG's site is offline now but i still have a copy of his ECDSA library somewhere here if you want it.

if you know c/c++, there's a simple implementation on codeproject (attached the code which requires login)

http://www.codeproject.com/KB/security/Elliptic_Curves.aspx

Certicom have tutorial http://www.certicom.com/index.php/ecc

you might want to study RSA first before ECC as RSA is much easier to implement and understand.
i have some implementations of RSA in plain C and Java which use just Big Number libraries.

[bozo]

can't attach library files by WiteG (too big)

the lite version doesn't include source code

https://rapidshare.com/files/3025513853/ecdsa128_lite.zip
https://rapidshare.com/files/791445027/ecdsa128.zip

[ragdog]

What is the different about eccdlp and ecp?

thanks for you sources

[bozo]

I'm not the right person to ask ...

The ECP library contains all the Elliptic Curve arithmetic functions in Galois Field
ECDLP or Discrete Logorithm Problem is what in theory makes ECC strong against cryptanalytic attacks.

You can solve DLP using something like Pollard Rho algorithm.

A math or cryptography forum would offer more insight...assuming they will answer you without being condescending.  :wink

[Astro]

Some important points to note:

* ECC is subject to patents http://en.wikipedia.org/wiki/ECC_patents

* YOU MUST CHOOSE YOUR ALGORITHM CAREFULLY.

* NOT ALL EC ARE SECURE

* THERE IS A QUESTION MARK OVER THE SECURITY OF THE NIST/NSA ECC SUGGESTED FUNCTIONS

ECC is a very deep area to be studying and will require quite a bit of time to unravel. I started researching it then stopped, as the math was simply over my head. One thing that I found very quickly was that to find a secure form is hard, and it is possible there is another related algorithm that can be used to encrypt/decrypt data that used the original algo (this is the source of the question over security of the NIST/NSA suggested form, with this second function being chosen at the time of the first).

ECC looks very promising, but there are too many question marks over how secure it actually is. The situation with patents doesn't help. There is an argument that ECC was chosen as it can be effectively back-doored without trace.