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This book offers a mathematical foundation for modern cryptography. It is primarily intended as an introduction for graduate students. Readers should have basic knowledge of probability theory, but familiarity with computational complexity is not required. Starting from Shannon's classic result on secret key cryptography, fundamental topics of cryptography, such as secret key agreement, authentication, secret sharing, and secure computation, are covered. Particular attention is drawn to how correlated randomness can be used to construct cryptographic primitives. To evaluate the efficiency of such constructions, information-theoretic tools, such as smooth min/max entropies and information spectrum, are developed. The broad coverage means the book will also be useful to experts as well as students in cryptography as a reference for information-theoretic concepts and tools.
In Chapter 6, RSA, DH and DSA in the Wild, Nadia Heninger outlines the various cryptographic pitfalls one can – but really should not – make in practice. Often it is possible to bypass the 'hard' mathematical problem a cryptosystem is based upon, and instead take advantage of implementation, deployment or protocol mistakes to extract the private key. Often, the techniques used are excellent examples of the interplay of mathematics and computer science, requiring a combination of ingenuity to find the core idea and perseverance to exploit the weakness in practice. Heninger gives a wide-ranging overview of the multitude of cryptographic implementation vulnerabilities that have been found in the past decades and their impact in practice, including a fair number where she was personally involved in identifying the vulnerability. In Chapter 6, she wonders whether, after several decades of implementation chaos and catastrophic vulnerabilities, we are doomed, but concludes that there is hope yet by bringing into practice the lessons learned.