We introduce a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and customized for its use in quantum cryptography. We propose new strong security definitions for quantum 1-out-of-2 oblivious transfer (OT) and quantum bit commitment (BC) and provide a technique for proving security against dishonest receivers/committers. The uncertainty relation is used to prove security in this strong sense of protocols for OT and BC in the bounded quantum-storage model. Joint work with Ivan Damgaard, Serge Fehr, Christian Schaffner, and Renato Renner.