  [Shortened abstract:] This thesis investigates the importance of quantum
memory in quantum cryptography, concentrating on quantum key distribution
schemes.
  In the hands of an eavesdropper -- a quantum memory is a powerful tool,
putting in question the security of quantum cryptography; Classical privacy
amplification techniques, used to prove security against less powerful
eavesdroppers, might not be effective when the eavesdropper can keep quantum
states for a long time. In this work we suggest a possible direction for
approaching this problem. We define strong attacks of this type, and show
security against them, suggesting that quantum cryptography is secure. We start
with a complete analysis regarding the information about a parity bit (since
parity bits are used for privacy amplification). We use the results regarding
the information on parity bits to prove security against very strong
eavesdropping attacks, which uses quantum memories and all classical data
(including error correction codes) to attack the final key directly.
  In the hands of the legitimate users, a quantum memory is also a useful tool.
We suggest a new type of quantum key distribution scheme where quantum memories
are used instead of quantum channels. This scheme is especially adequate for
networks of many users. The use of quantum memory also allows reducing the
error rate to improve large scale quantum cryptography, and to enable the
legitimate users to work with reasonable error rate.
