2020-so-far yes, Grover's algorithm would only effectively reduce key sizes by half:
but there isn't a mathematical proof either.
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The Advanced Encryption Standard (AES) is a symmetric encryption algorithm that is widely used for securing data. It was established by the U.S. National Institute of Standards and Technology (NIST) in 2001 and has become the standard for encrypting sensitive information across various applications, including government, financial, and commercial systems.