"The Mathematics of Secrets takes readers on a tour of the mathematics behind cryptography--the science of sending secret messages. Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers operate, as he focuses on both code making and code breaking. He discusses the majority of ancient and modern ciphers currently known, beginning by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. He explores polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, ciphers involving exponentiation, and public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. Only basic mathematics up to high school algebra is needed to understand and enjoy the book." -- adapted from jacket flap

Introduction to ciphers and substitution. Alice and Bob and Carl and Julius: terminology and Caesar Cipher ; Key to the matter: generalizing the Caesar Cipher ; Multiplicative ciphers ; Affine ciphers ; Attack at dawn: cryptanalysis of sample substitution ciphers ; Just to get up that hill: polygraphic substitution ciphers ; Known-plaintext attacks ; Looking forward -- Polyalphabetic substitution ciphers. Homophonic ciphers ; Coincidence or conspiracy? ; Alberti ciphers ; It's hip to be square: Tabula Recta or Vigenère Square ciphers ; How many is many? ; Determining the number of alphabets ; Superman is staying for dinner: superimposition and reduction ; Products of polyalphabetic ciphers ; Pinwheel machines and rotor machines ; Looking forward -- Transposition ciphers. This is Sparta! The Scytale ; Rails and routes: geometric transposition ciphers ; Permutations and permutation ciphers ; Permutation products ; Keyed columnar transposition ciphers ; Determining the width of the rectangle ; Anagramming ; Looking forward -- Ciphers and computers. Bringing home the bacon: polyliteral ciphers and binary numerals ; Fractionating ciphers ; How to design a digital cipher: SP-networks and feistel networks ; Data encryption standard ; Advanced encryption standard ; Looking forward -- Stream ciphers. Running-key ciphers ; One-time pads ; Baby you can drive my car: autokey ciphers ; Linear feedback shift registers ; Adding nonlinearity to LFSRs ; Looking forward -- Ciphers involving exponentiation. Encrypting using exponentiation ; Fermat's little theorem ; Decrypting using exponentiation ; Discrete logarithm problem ; Composite moduli ; Euler Phi function ; Decryption with composite moduli ; Looking forward -- Public-key ciphers. Right out in public: the idea of public-key ciphers ; Diffie-Hellman key agreement ; Asymmetric-key cryptography ; RSA ; Priming the pump: primality testing ; Why is RSA a (Good) public-key system? ; Cryptanalysis of RSA ; Looking forward -- Other public-key systems. Three-pass protocol ; ElGamal ; Elliptic curve cryptography ; Digital signatures ; Looking forward -- Future of cryptography. Quantum computing ; Postquantum cryptogaphy ; Quantum cryptography ; Looking forward