Modern cryptography provides essential techniques for securing information and protecting data. In the first part, this book covers the key concepts of cryptography at the undergraduate level, from encryption and digital signatures to cryptographic protocols. In the second, more advanced topics covered, such as security a little one-way functions and pseudorandom generators bit computing is perfect. Typical examples of provably secure encryption and signature schemes and their security proof is given. The second edition contains corrections, revisions and new material, including a full description of AES, an extended section on cryptographic hash functions, a new section on evidence of a random oracle, and a new section on public key encryption scheme is provably secure against adaptive chosen-ciphertext attack.