Introduction to Cryptography

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The first part of this book introduces key cryptography concepts at the undergraduate level, covering encryption, digital signatures, and cryptographic protocols. Essential techniques are illustrated through protocols for key exchange, user identification, electronic elections, and digital cash. The second part delves into advanced topics, including the bit security of one-way functions and computationally perfect pseudorandom bit generators, with a focus on the security of cryptographic schemes. It provides examples of provably secure encryption and signature schemes along with their security proofs. While the text emphasizes mathematical foundations, no prior math background is required, as relevant algebra, number theory, and probability theory are included in the appendix. Each chapter concludes with exercises for practice. The second edition features a complete description of AES, an expanded section on cryptographic hash functions, and new sections on random oracle proofs and public-key encryption schemes secure against adaptively-chosen-ciphertext attacks. The third edition further extends the content with topics like elliptic curve cryptography, Paillier encryption, quantum cryptography, the SHA-3 standard, an expanded section on electronic elections and Internet voting, mix nets, and zero-knowledge proofs of shuffles. This resource is suitable for undergraduate and graduate students in computer science, mathematics, a