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The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography-the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.

Cryptography --- Ciphers. --- Computer security. --- Mathematics. --- Adaptive chosen-ciphertext attack. --- Advanced Encryption Standard. --- Affine cipher. --- Alice and Bob. --- Autokey cipher. --- Block cipher mode of operation. --- Block cipher. --- Block size (cryptography). --- Brute-force attack. --- Brute-force search. --- Caesar cipher. --- Calculation. --- Chosen-ciphertext attack. --- Chosen-plaintext attack. --- Cipher. --- Ciphertext-only attack. --- Ciphertext. --- Codebook. --- Communication Theory of Secrecy Systems. --- Computational problem. --- Confusion and diffusion. --- Correlation attack. --- Craig Gentry (computer scientist). --- Cryptanalysis. --- Cryptogram. --- Cryptographic engineering. --- Cryptographic hash function. --- Cryptography Research. --- Cryptography. --- Cryptosystem. --- Data Encryption Standard. --- Differential cryptanalysis. --- Diffie–Hellman key exchange. --- Discrete logarithm. --- Disquisitiones Arithmeticae. --- Dual EC DRBG. --- ElGamal encryption. --- Elliptic curve cryptography. --- Encryption. --- Enigma machine. --- Euler's theorem. --- Fast Software Encryption. --- Feistel cipher. --- Fermat's little theorem. --- Forward secrecy. --- Grover's algorithm. --- Hill cipher. --- Homomorphic encryption. --- Hyperelliptic curve cryptography. --- Information theory. --- Initialization vector. --- International Association for Cryptologic Research. --- Kerckhoffs's principle. --- Key (cryptography). --- Key schedule. --- Key size. --- Keystream. --- Known-plaintext attack. --- Lattice problem. --- Linear cryptanalysis. --- Logjam (computer security). --- Mathematical problem. --- Mathematician. --- Mental poker. --- Merkle's Puzzles. --- Monte Carlo algorithm. --- Multiple encryption. --- NSA Suite B Cryptography. --- Nonlinear feedback shift register. --- Number theory. --- Padding (cryptography). --- Permutation box. --- Permutation. --- Plaintext. --- Polyalphabetic cipher. --- Post-quantum cryptography. --- Precomputation. --- Probabilistic encryption. --- Product cipher. --- Public-key cryptography. --- Quantum algorithm. --- Quantum cryptography. --- Quantum key distribution. --- RSA (cryptosystem). --- RSA problem. --- Related-key attack. --- S-box. --- Security level. --- Shor's algorithm. --- Sign (mathematics). --- Spyware. --- Stream cipher. --- Substitution cipher. --- Symmetric-key algorithm. --- Transposition cipher. --- VIC cipher. --- Variable (computer science). --- Vigenère cipher. --- Vulnerability (computing).