Existing implementations of public-key cryptography, a basis for many modern safety functions similar to secure monetary transactions over the Internet. However, the most effective identified quantum algorithm for this downside, Shor’s algorithm, does run in polynomial time, though this does not indicate where the issue lies with respect to non-quantum complexity classes. In 1975, Richard E. Ladner confirmed that if P ≠ NP then there exist problems in NP that are neither in P nor NP-complete. The graph isomorphism problem, the discrete logarithm problem and the integer factorization drawback are examples of problems believed to be NP-intermediate.
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