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Foundations of Cryptography: A Primer (Foundations and Trends in Theoretical Computer Science,)

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The vast expansion and rigorous treatment of cryptography is one of the major achievements of theoretical computer science. In particular, concepts such as computational indistinguishability, pseudorandomness and zero-knowledge interactive proofs were introduced, classical notions such as secure encryption and unforgeable signatures were placed on sound grounds, and new (unexpected) directions and connections were uncovered. Indeed, modern cryptography is strongly linked to complexity theory (in contrast to “classical” cryptography which is strongly related to information theory).

Modern cryptography is concerned with the construction of information systems that are robust against malicious attempts to make these systems deviate from their prescribed functionality. The prescribed functionality may be the private and authenticated communication of information through the Internet, the holding of tamper-proof and secret electronic voting, or conducting any “fault-resilient” multiparty computation. Indeed, the scope of modern cryptography is very broad, and it stands in contrast to “classical” cryptography (which has focused on the single problem of enabling secret communication over insecure communication media).

The design of cryptographic systems is a very difficult task. One cannot rely on intuitions regarding the “typical” state of the environment in which the system operates. For sure, the adversary attacking the system will try to manipulate the environment into “untypical” states. Nor can one be content with counter-measures designed to withstand specific attacks, since the adversary (which acts after the design of the system is completed) will try to attack the schemes in ways that are different from the ones the designer had envisioned. The validity of the above assertions seems self-evident, but still some people hope that in practice ignoring these tautologies will not result in actual damage. Experience shows that these hopes rarely come true; cryptographic schemes based on make-believe are broken, typically sooner than later.
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