In this chapter we briefly discuss the goals of cryptography (Section 1.1). In particular, we discuss the basic problems of secure encryption, digital signatures, and fault-tolerant protocols. These problems lead to the notions of pseudorandom generators and zero-knowledge proofs, which are discussed as well.

Our approach to cryptography is based on computational complexity. Hence, this introductory chapter also contains a section presenting the computational models used throughout the book (Section 1.3). Likewise, this chapter contains a section presenting some elementary background from probability theory that is used extensively in the book (Section 1.2).

Finally, we motivate the rigorous approach employed throughout this book and discuss some of its aspects (Section 1.4).

Teaching Tip. Parts of Section 1.4 may be more suitable for the last lecture (i.e., as part of the concluding remarks) than for the first one (i.e., as part of the introductory remarks). This refers specifically to Sections 1.4.2 and 1.4.3.

Cryptography: Main Topics

Historically, the term “cryptography” has been associated with the problem of designing and analyzing encryption schemes (i.e., schemes that provide secret communication over insecure communication media). However, since the 1970s, problems such as constructing unforgeable digital signatures and designing fault-tolerant protocols have also been considered as falling within the domain of cryptography. In fact, cryptography can be viewed as concerned with the design of any system that needs to withstand malicious attempts to abuse it.