Intro: 'life hung on the strength of a cipher', invisible ink, microdot, main branches of cryptography, Mono-alphabetic substitution cipher, Frequency analysis, atbash, Giovani Soro, Battista Alberti, Poly-alphabetic substitution cipher, Vignere Cipher, Blaise de Vignere, Homophonic substitution cipher, The Great Cipher, The Black Chambers, Charles Babbage & breaking of Vignere Cipher, Playfair Cipher, Pigpen Cipher, Pinprick encryption, Edgar Allan Poe, The Gold Bug, Book Cipher, Beale Cipher, Marconi, Zimmermann telegram, One-time pad cipher - 'the holy grail of cryptogrpahy', Cipher Disk, Enigma (1918), Arthur Scherbius (german) & Enigma machine, Day-key & Message-key, Breaking of Enigma, Marian Rejeswski (polish), Bombes, Bletchley Park, Alan Turing, Universal Turing Machine, 'On Computable Numbers' (1937), 'Dip the Apple in the Brew; Let the sleeping death seep through', GCHQ (british), Purple (Japanese Machine Cipher), SIGABA (American) cipher machine, Navajo Code talkers, Deciphering Hieroglyphics (Egypt), Hieratic, Demotic, Coptic, Phonographs, Semagrams, The Rosetta Stone, Thomas Young (English), Jean Francois Champolian (France), rebus principl, Deciphering Linear B (cretan script), Sir Arthus Evans, Michael Ventris, John Chadwick , 'Everest of Greek Archaeology', Colossus, Lorenz Cipher (german), Eniac, Lucifer (IBM), DES (Data Encryption Standard0, Key distribution, COMSEC, Whitfield Diffie & Martin Hellman, 'God Rewards Fools', one-way functions, Modular Arithmetic/Clock arithmetic, Diffie-Hellman-Merkle key exchange system, Public Key Cryptography, RSA, James Ellis, Clifford Cocks, Malcolm Williamson, PGP, Phil Zimmermann, IDEA, e-commerce, key escrow, Certification authorities, Verisign, Trusted Third Parties (TTPs), Key recovery, A quantum leap into the future (incomplete...).
Introduction, Taniyama-Shimura conjecture, 'The last problem' by Eric Temple Bell, Pythagoras of Samos, "Life, Prince Leon, may well be compared...", Rational numbers, perfect numbers, excessive numbers, Pythagoras and the underlying principles of musical harmony, Pi, "Rivers have a tendency towards an even more loopy path because slightest curve will lead to faster currents on the outer side which will in turn result in more erosion and sharper bend...", Pythagoras theorem, absolute proof, axiom, theorem, hypothesis; end of Pythagoras; Pythagorean triplets; from Pythagoras theorem to Fermat's theorem; the riddler - Pierre de Fermat, Alexandrian library, Euclid, Mathematics department at Alexandrian University; Euclid Elements - the most successful textbook in history, Proof by contradiction, Euclid's proof that sqrt(2) is irrational; pi - the most famous irrational number, Diophantus of Alexandria - the riddle said to have been carved on his tomb; Arithmetica - 6 of 13 would survive, Birth of a riddle, Friendly numbers or amicable numbers (220, 284); sociable numbers; Euclid's proof that there are an infinite number of Pythagorean triplets; "In the margin of the Arithmetica, next to problem 8, he made a note of his observation: cubem autem in duos cubos, aut quadratoquadratum in duous quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatum in duous eusdem nominis fas est dividere", "I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain", The last theorem published at last; Clement Samuel; Fermat's prime theorem; 'The devil and the simon Flagg', A mathematical disgrace.
Introduction, Disquisitiones Arithmeticae by Carl Friedrich Gauss, Euclid's Elements, remark on the notation, properties, remainder operator in computer science, applications, modular multiplicative inverse, modular exponentiation, right-to-left binary method, modular_power pseudocode, example.
Introduction, standard Euclidean algorithm, Euclidean division, Bezout's coefficients, the case of more than two numbers, computing multiplicative inverses in modular structures, applications, another way to look at the extended Euclidean algorithm, An application of modular multiplicative inverse - Affine Cipher.
Introduction, 2^67-1 Mersenne Number, fundamental theorem of arithmetic, public key cryptography, Whit Diffie and Martin Hellman, RSA and MIT trio, 'New Directions in Cryptography', a cryptographic card trick, Fermat's little theorem, Euler's Totient theorem, RSA - a worked out example, Euler's theorem, Fermat's little theorem, Proof of correctness of RSA algorithm - using Fermat's little theorem and using Euler's theorem, integer factorization and RSA problem.
Overview, unecrypted telnet session, public & private keys, key management, usage, sftp, scp, history and development, Tatu Ylonen, openssh and osh, version 1 and 2, uses of ssh, architecture, vulnerabilities, key concepts, id_rsa.pub, authorized_keys, fingerprints, host keys, pki, changed host key, ssh-keygen, passphrase, slogin, ssh-agent, running commands on remote systems, scp (secure copy), remote commands, x11 forwarding, config files for ssh, rsa authentication, ssh-agent, starting the agent, adding and removing keys, using the agent, exiting the agent, port forwarding.
Introduction, history, forward secrecy property, idea of the algorithm, cryptographic explanation, modular arithmetic properties, D-H problem, computational complexity, birth of pulic key cryptosystems.