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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A symmetric-key algorithm is a type of cryptographic algorithm where the same key is used for both encryption and decryption of data. This means that both the sender and the receiver must possess the same secret key in order to encrypt and decrypt messages securely. ### Key Characteristics of Symmetric-Key Algorithms: 1. **Single Key Use**: The same key is used for both operations, which means that key management and distribution become crucial aspects of maintaining security.