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w-intro - Chapter 1 Introduction Historically cryptography...

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Chapter 1 Introduction Historically, cryptography arose as a means to enable parties to maintain privacy of the information they send to each other, even in the presence of an adversary with access to the communication channel. While providing privacy remains a central goal, the field has expandeded to encompass many others, including not just other goals of communication security, such as guaranteeing in- tegrity and authenticity of communications, but many more sophisticated and fascinating goals. Once largely the domain of the military, cryptography is now in widespread use, and you are likely to have used it even if you don’t know it. When you shop on the Internet, for example to buy a book at www.amazon.com , cryptography is used to ensure privacy of your credit card number as it travels from you to the shop’s server. Or, in electronic banking, cryptography is used to ensure that your checks cannot be forged. Cryptography has been used almost since writing was invented. For the larger part of its history, cryptography remained an art, a game of ad hoc designs and attacks. Although the field retains some of this flavor, the last twenty-five years have brought in something new. The art of cryptography has now been supplemented with a legitimate science. In this course we shall focus on that science, which is modern cryptography. Modern cryptography is a remarkable discipline. It is a cornerstone of computer and communi- cations security, with end products that are imminently practical. Yet its study touches on branches of mathematics that may have been considered esoteric, and it brings together fields like number theory, computational-complexity theory, and probabiltity theory. This course is your invitation to this fascinating field. 1.1 Goals and settings Modern cryptography addresses a wide range of problems. But the most basic problem remains the classical one of ensuring security of communication across an insecure medium. To describe it, let’s introduce the first two members of our cast of characters: our sender, S , and our receiver, R . (Sometimes people call these characters Alice, A , and Bob, B . Alice and Bob figure in many works on cryptography. But we’re going to want the letter A for someone else, anyway.) The sender and receiver want to communicate with each other. The ideal channel. Imagine our two parties are provided with a dedicated, untappable, im- penetrable pipe or tube into which the sender can whisper a message and the receiver will hear
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2 INTRODUCTION S R A x x x x x x Figure 1.1: Several cryptographic goals aim to imitate some aspect of an ideal channel connecting a sender S to a receiver R . it. Nobody else can look inside the pipe or change what’s there. This pipe provides the perfect medium, available only to the sender and receiver, as though they were alone in the world. It is an “ideal” communication channel from the security point of view. See Fig. 1.1.
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