Quantum computers threaten asymmetric cryptography like RSA and ECDSA through Shor's algorithm, but leave symmetric algorithms like AES-128 and SHA-256 unaffected. A common misconception suggests quantum computers "halve" symmetric key security, requiring 256-bit keys for 128-bit protection. This misunderstanding misapplies Grover's algorithm, which actually provides less speedup than commonly believed when applied to symmetric cryptography.

Grover's algorithm offers only quadratic speedup for searching unstructured functions, but this benefit diminishes significantly when attempting to parallelize attacks against symmetric keys. Unlike classical brute force attacks, partitioning the search space degrades the quadratic advantage. Breaking AES-128 would require an impractical amount of parallel quantum circuits running for years, making 128-bit symmetric keys safe against quantum attacks.

The computational cost of breaking AES-128 with Grover's algorithm is approximately 430 quadrillion times more expensive than breaking 256-bit elliptic curves with Shor's algorithm. NIST confirms AES-128's safety for post-quantum security, designating it as a Category 13 post-quantum algorithm. Standardization bodies agree that symmetric key sizes remain unchanged in the post-quantum transition.