Encryption and Decryption

Encryption and Decryption

DOI: 10.4018/978-1-4666-1649-3.ch002
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Abstract

As the foundation of all security enhanced systems, encryptions and decryptions are defined, and homomorphic (additive or multiplicative), probabilistic, commutative, and verifiable features are extracted as the desirable ones of encryption and decryption algorithms for developing secure anonymous systems. Also encryption and decryption algorithms are classified and onetime pad, permutation and substitution, RSA, and ElGamal are introduced as typical algorithms. Among them, onetime pad, RSA, and ElGamal are extensively used to develop secure anonymous systems in the remainder of this book.
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Introduction

As the bases of the following chapters, this chapter discusses various kinds of encryption and decryption algorithms. A typical example, in which encryption and decryption algorithms are required, is communication between two entities. When entity Q wants to receive messages from entity P, while protecting them from wiretappings, Q informs P of the algorithm to encrypt messages through usually an expensive and inefficient communication channel that is protected from wiretappings (e.g. an isolated private channel) in advance. After that, P encrypts its message M by the encryption algorithm received from Q so that no one except Q that knows the decryption algorithm can understand the meaning of M even someone eavesdrops on it, and sends M in its encrypted form through a usual inexpensive and efficient communication channel, e.g. through the Internet. Then, only Q can decrypt the message sent from P, and consequently can understand the meaning of M. The important thing here is that the encryption algorithm must be transferred more easily than M itself. If the encryption algorithm and the message are equally difficult to transfer, P may send M directly to Q through the expensive and inefficient communication channel in the same way as Q sends the encryption algorithm. Namely, P does not need to encrypt M.

Encryption and decryption algorithms used in the above communication are the most fundamental component of information security, i.e. they are used not only in protecting messages from wiretappings but also in protecting information from unauthorized modifications, in confirming honest behaviours of entities and almost in every security enhanced activity in both non-anonymous and anonymous information systems as shown in later chapters. However in anonymous systems, encryptions and decryptions are carried out under environments different from in usual non-anonymous systems, e.g. frequently information is both encrypted and decrypted by same entities, also, it is not rare that entities must ask not completely trusted other entities to encrypt their information, or all entities are required not to know correspondences between information and their encrypted forms. Therefore encryption and decryption algorithms for anonymous systems are required to have different features from the ones required in usual non-anonymous systems. There are cases where important constraints of encryption and decryption algorithms (e.g. algorithms must be transferred easily as just mentioned above) can be relaxed, and contrarily, some other requirements that are not important in usual systems become important. Consequently, not only the modern encryption and decryption algorithms but also various legacy ones can be or must be exploited to develop practical anonymous application systems. To confirm these circumstances, this chapter firstly summarizes desirable features of encryption and decryption algorithms; then in later sections, various kinds of algorithms are discussed especially in terms of these features.

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