quantum computers finding polynomial time algorithm solving dihedral hidden subgroup problem would break many lattice based cryptosystems well studied open problem proven applying grover 's algorithm break symmetric secret key algorithm brute force requires time equal roughly sup ''n'' sup invocations underlying cryptographic algorithm compared roughly sup ''n'' sup classical case ref name bennett ref meaning symmetric key lengths effectively halved aes would security attack using grover 's algorithm aes classical brute force search see ''key size'' quantum cryptography could potentially
Formal science Computer science Quantum computing