41 Crypto Topics and Applications Ii

In this chapter we continue our exposition of the crypto topics which was begun in the previous chapter. This chapter covers: Secret Sharing, Threshold Cryptography, Signature Schemes, and nally Quantum Key Distribution and Quantum Cryptography. As in the previous chapter, we have focussed only on the essentials of each topic. We have included in the bibliography suucient items which can be consulted for further details. First we give a synopsis of the topics which are discussed in this chapter. Secret sharing is concerned with the problem of how to distribute a secret among a group of participating individuals, or entities, so that only pre-designated collections of individuals are able to recreate the secret by collectively combining the parts of the secret which were allocated to them. There are numerous applications of secret sharing schemes in practice. One example of secret sharing occurs in banking. For instance, the combination to a vault may be distributed in such a way that only speciied collections of employees can open the vault by pooling their portions of the combination. In this way the authority to initiate an action, e.g., the opening of a bank vault, is divided for the purposes of providing security and for added functionality such as auditing if required. Threshold cryptography is a relatively recently studied area of cryptography. It deals with situations where the authority to initiate or perform cryptographic operations is distributed amongst a group of individuals. Many of the standard operations of single-user cryptography have counterparts in threshold cryptography. Signature schemes deal with the problem of generating and verifying (electronic) signatures for documents. A sub-class of signature schemes is concerned with the shared-generation and shared