Introduction to cryptography

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The first part of this book introduces key concepts of cryptography at the undergraduate level, covering topics such as encryption, digital signatures, and cryptographic protocols. It demonstrates essential techniques 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 strong focus on the security of cryptographic schemes. Examples of provably secure encryption and signature schemes, along with their security proofs, are provided. While the book emphasizes mathematical foundations, no specialized background in mathematics is required, as necessary algebra, number theory, and probability theory are included in the appendix. Each chapter concludes with exercises. The second edition features a complete description of AES, an expanded section on cryptographic hash functions, and new sections on random oracle proofs and secure public-key encryption against adaptively-chosen-ciphertext attacks. The third edition further extends the content with new topics such as 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 book is suitable for undergraduate and graduate students in compu