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The Data Encryption Standard (DES) is no longer secure because of its small key size. One way to augment the keyspace is to perform multiple encryptions with DES. This paper examines the cryptographic consequences of multiple encryptions with DES through two simplified DES algorithms. Both simplified algorithms, under multiple encryptions, generate the alternating group of permutations on the message space. Moreover, equivalent keys and key pairs are rare in both cases. These facts support past work that has shown that performing multiple encryptions with DES adds keyspace by demonstrating that the increase in keyspace is significant. [ABSTRACT FROM AUTHOR]

The paper is intended to be a survey of all the important aspects and results that have shaped the field of quantum computation and quantum information. The reader is first familiarized with those features and principles of quantum mechanics providing a more efficient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction are then discussed. Prospects for building a practical quantum computer are also analyzed. [ABSTRACT FROM AUTHOR]