There was some discussion a few years back on this forum about possibly implementing elliptic curve cryptography to replace RSA. We all know that RSA, which is based on factoring, is more easily liable to a brute force attack. The answer to counter this is increasing the key size. The problem with this, however, is that it can slow down the service.
ECC is the talk by everyone now because it offers (arguably) better security than RSA with faster processing. 512bit ECC is equivalent to 256bit key (symmetric), unlike RSA which requires over a 15000 key size to equal 256bit key (symmetric).
My understanding is that the NSA recommends a 1:1 approach. Put differently, a 128bit (symmetric) key should be protected by a 3072bit (asymmetric) key.
This is all but impossible (in practice) with RSA and 256bit symmetric encryption.
It would seem ECC is superior to RSA. However, with all the ado about ECC and it being pushed by the NSA, some have speculated (including Bruce Schneier) that the NSA "may" more easily break ECC (perhaps due to some arcane knowledge) and that is why it is being pushed (possibly).
With all its faults, RSA has been around forever and has been studied to death. ECC, on the other hand, has been much less analyzed.
Could ECC be a NSA trap? Does the answer lie in using very large keyswhether ECC or RSA?
Elliptic Curve Cryptography

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Re: Elliptic Curve Cryptography
The security ECC doesn't depend only on key size. It depends on parameters of the elliptic curves too.Could ECC be a NSA trap?
Some NIST recommendation of curve parameters are suspected to be influenced by NSA.
But there are recommendations by independent crypto experts available too like "Curve25519" by Daniel J. Bernstein or "Edwards coordinates" by Harold M. Edwards (improved by Bernstein/Lange), well documented and secure.
In my opinion ECC can be a replacement for RSA, if large key size was required. The computational complexity of RSA increases with n^3 with increasing key size n. It is not useful to increase the key size for RSA without limits.
Re: Elliptic Curve Cryptography
Choosing safe curves for ellipticcurve cryptography: http://safecurves.cr.yp.to/
Some parameter sets are safe, some parameter sets are broken.
By: Daniel J. Bernstein and Tanja Lange
Some parameter sets are safe, some parameter sets are broken.
By: Daniel J. Bernstein and Tanja Lange
Re: Elliptic Curve Cryptography
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Re: Elliptic Curve Cryptography
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Re: Elliptic Curve Cryptography
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