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1.2 What is cryptography?

As the field of cryptography has advanced, the dividing lines for what is and what is not cryptography have become blurred. Cryptography today might be summed up as the study of techniques and applications that depend on the existence of difficult problems. Cryptanalysis is the study of how to compromise (defeat) cryptographic mechanisms, and cryptology (from the Greek kryptós lógos, meaning ``hidden word'') is the discipline of cryptography and cryptanalysis combined. To most people, cryptography is concerned with keeping communications private. Indeed, the protection of sensitive communications has been the emphasis of cryptography throughout much of its history [Kah67]. However, this is only one part of today's cryptography.

Encryption is the transformation of data into a form that is as close to impossible as possible to read without the appropriate knowledge (a key; see below). Its purpose is to ensure privacy by keeping information hidden from anyone for whom it is not intended, even those who have access to the encrypted data. Decryption is the reverse of encryption; it is the transformation of encrypted data back into an intelligible form.

Encryption and decryption generally require the use of some secret information, referred to as a key. For some encryption mechanisms, the same key is used for both encryption and decryption; for other mechanisms, the keys used for encryption and decryption are different (see Question 2.1.1).

Today's cryptography is more than encryption and decryption. Authentication is as fundamentally a part of our lives as privacy. We use authentication throughout our everyday lives - when we sign our name to some document for instance - and, as we move to a world where our decisions and agreements are communicated electronically, we need to have electronic techniques for providing authentication.

Cryptography provides mechanisms for such procedures. A digital signature (see Question 2.2.2) binds a document to the possessor of a particular key, while a digital timestamp (see Question 7.11) binds a document to its creation at a particular time. These cryptographic mechanisms can be used to control access to a shared disk drive, a high security installation, or a pay-per-view TV channel.

The field of cryptography encompasses other uses as well. With just a few basic cryptographic tools, it is possible to build elaborate schemes and protocols that allow us to pay using electronic money (see Question 4.2.1), to prove we know certain information without revealing the information itself (see Question 2.1.8), and to share a secret quantity in such a way that a subset of the shares can reconstruct the secret (see Question 2.1.9).

While modern cryptography is growing increasingly diverse, cryptography is fundamentally based on problems that are difficult to solve. A problem may be difficult because its solution requires some secret knowledge, such as decrypting an encrypted message or signing some digital document. The problem may also be hard because it is intrinsically difficult to complete, such as finding a message that produces a given hash value (see Question 2.1.6).

Surveys by Rivest [Riv90] and Brassard [Bra88] form an excellent introduction to modern cryptography. Some textbook treatments are provided by Stinson [Sti95] and Stallings [Sta95], while Simmons provides an in-depth coverage of the technical aspects of cryptography [Sim92]. A comprehensive review of modern cryptography can also be found in Applied Cryptography [Sch96]; Ford [For94] provides detailed coverage of issues such as cryptography standards and secure communication.

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