Asymmetric encryption that is secure for (almost) any foreseeable future Recently, I've been reading a couple of papers about building cryptosystems that are secure for up to 30 years. But for some applications, this seems a bit low to me. So I am wondering if considering the current state of the art in cryptography and computing power evolution forecasts, one could instead build a public-key encryption system, running on today's consumer hardware, which is secure for any foreseeable future.

Of course, written like this, the problem is too broad, so my specific criteria are as follows:


Keys are permanent, ciphertext which has been encrypted today must remain secure
Security is broken if an attacker can reliably decipher text which has been encrypted with the public key, without possessing the private key
Scenarios in which the attacker gets a hold of the private key by stealing, torture, and other means of extracting it from the rightful owner, are not considered a breach of security
My (very generous) upper bound for performance forecast realism is 1000 years in the future
I personally do not consider general-purpose quantum computers, based on logic gates operating on a large number of entangled qubits, to be viable in any foreseeable future, so security against them is just a nice extra
More specialized quantum computing systems like D-wave's quantum annealing, however, which do not rely on many-particle entanglement, are within the realm of possibilities
Attacker may be considered to have access to exabytes of ciphertext and terabytes of plain text - ciphertext pairs
Attacker may have access to state-of-the-art computing power, like the supercomputers of his generation
It must be possible to transfer public keys over the Internet within a reasonable time (absolute maximum is 1 day on a low-end 30 kB/s Internet connection -> 2GB), but they do not need to be transmitted frequently so it is acceptable if the keys are unusually big
Encryption must be fast on today's hardware, let's say 30 MB/s on a high-end laptop as a lower performance bound


Is this totally crazy, or can it be done using today's knowledge in cryptographic algorithms + implementations which are either available today or can be made available in the near future?
I think that there is no chance of getting such an asymmetric cipher simply because you forgot about science.

The security on todays asymmetric cryptography is mostly based on the assumption that some mathematical algorithms cannot be reversed (e.g. the discrete logarithm or integer factorization).

If mathematics solves this problems then the algorithm is broken.

Such a breakthrough in mathematics can occur (e.g. for Fermat's Last Theorem in 1994).

So the major problem with assuring asymmetric cryptography as secure is to assure that no such breakthrough will occur.