Understanding which problems quantum computers can solve faster than classical computers is a fundamental problem. It is known that quantum computers can break widely used cryptosystems, including those used for e-commerce transactions, but finding new useful applications is a challenging and important task. It is equally important to determine which cryptosystems quantum computers cannot break. This is important since today's encrypted information should remain secure even after quantum computers have been built. This project will address these two issues. The first part will focus on finding new problems that have exponentially faster algorithms on quantum computers than on classical computers. Problems where a potential exponential speedup exists include graph isomorphism, the unique shortest lattice vector problem, and the nonabelian hidden subgroup problem. The second part of this project will study which classical cryptosystems remain secure in the presence of quantum computers. This requires understanding the limitations of quantum computers. Modern cryptography relies on assuming that certain problems cannot be solved on classical computers, and this set must also be identified for quantum computers. Some existing systems, such as lattice-based cryptosystems, have not been sufficiently studied. Other questions include the security of zero-knowledge proofs and pseudo-random number generators against quantum attacks.
|Effective start/end date||8/1/08 → 7/31/14|
- National Science Foundation: $512,000.00