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We can't trust RSA to encrypt our Emails so what is best post-quantum cryptography system as alternative for RSA which provide good security and don't be breakable? because McEliece cryptosystem looks break with 2^60.55 bit operations..

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You'll need a source for your McEliece statement. I'd expect the number of operations to depend on key sizes. If you're willing to use a large key, you should be able to reach any security level you like. – CodesInChaos Dec 7 '12 at 11:14

My impression is that there is no production ready post quantum scheme ATM.

NTRU seems to be decent (complete spec, reasonable parameter-sizes and performance), but I think it's patented. No idea about the licensing terms.

But whatever scheme you choose, don't use it instead of a conventional scheme(RSA, DH, ECDH) but in addition to a conventional scheme. If you use a good construction, your protocol will be as secure as the stronger of the schemes.

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Hasn't NTRU been broken several time by Faugère's work on Gröbner basis ? – Alexandre Yamajako Dec 7 '12 at 11:48
@AlexandreYamajako No idea. I don't really trust any of these new schemes, that's why I recommended using it in addition to a conventional scheme. – CodesInChaos Dec 7 '12 at 12:16
@CodeInChaos what construction were you thinking about ? I don't think composition is a terrible idea but there are exemples in which it breaks. Maybe pick $r$ at random then $m_0\gets r\oplus m$ and $m_1 \gets r$ ? – Alexandre Yamajako Dec 7 '12 at 13:38
@AlexandreYamajako The choice of construction depends on the application requirements. But if you just need a symmetric key, you could for example choose two random keys, encrypt each one with a different scheme, and use the hash of both as your symmetric key. – CodesInChaos Dec 7 '12 at 13:39
Or you could avoid avoid needing to rely on "random oracle"ness of the hash, and $\hspace{1.4 in}$ just use the xor of both as your symmetric key. $\:$ – Ricky Demer Dec 7 '12 at 22:41

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