ECC ( Elliptic Curve Cryptography) can be implemented in different methods, it is more complex than RSA. In addition, its discrete logarithm problem is more difficult to break than the factorization. The researchers have tried to attack ECC, but it is infeasible using the computational resources.
In present, the security strength of ECC is stronger than other public key cryptosystems.
Any help will be the great appreciation. Thanks.
I found a probably interesting article about ECC security at https://it.slashdot.org/firehose.pl?op=view&type=story&sid=13/09/11/1224252
Indeed ECC is safer than regular discrete log and factoring based systems (some attacks do not apply which allowed the use of shorter fields).
A good start with many pointers to the used curves: NIST and others, and a good introduction is, surprisingly, in Wikipedia https://en.wikipedia.org/wiki/Elliptic_curve_cryptography
I agree that ECC is a good choice among standardized, asymmetric algorithms until quantum computing becomes a practical reality. Then the game changes.
The best book I have found about Elliptic Curves is "Factorization and Primality Testing" its author is David Bressoud, Springer-Verlag. Other good documents as you know are available at NIST site.(www.nist.gov)
I think ECCs are safe enough, another choice could be Vernam-like algorithms.
I like ECC. But I need to know more about it. What is said about it here is absolutely true.
ECC is indeed much more secure and its implementation is now popular in various applications
Dear Davood,
Please see the following link about the Next-generation elliptic-curve cryptography :
https://cr.yp.to/talks/2016.02.18/slides-djb-20160218-4x3.pdf
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