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Mathematician warns US spies may be weakening next-gen encryption
(www.newscientist.com)
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Asymmetric key exchange works by utilising a complex math equation involving massive exponents that is easy to run to get an answer, but very hard to use that answer to get the numbers you started with.
With traditional computers, you essentially need to try every combination of numbers through trial and error to get the starting values.
Quantum computers are almost purpose built for this kind of math and can solve those types of problems exponentially faster than traditional computers.
However, for a symmetric key, there isn't an exchange that can be attacked, both sides already know the key.
There is still a quantum attack against symmetric key crypto like AES, but it just reduces the effective key size by half. If you use long enough keys (256 bits) you're still fine.