Vigenère’s Cryptosystem Le chiffre indéchiffrable April 6, 2005 copyright Kevin O'Bryant

copyright Kevin O'Bryant Office Hours I have lunch in Revelle cafeteria after class Barry will have office hours in AP&M 6402c, Tuesdays noon-2pm and Fridays 8am-10am (except this week, when Friday will be replaced with Thursday 2pm-4pm) April 6, 2005 copyright Kevin O'Bryant

A Genetic Algorithm Q(k):=( (Ni-Fi)2+  (Nij-Fij)2)-1 1. Generate 100 random keys (and call them “adults”). 2. Assign to each adult a quality: Q(k):=( (Ni-Fi)2+  (Nij-Fij)2)-1 where Fi is the frequency in English of the i-th letter, and Fij is the percentage of letter i which are followed by j, and Ni and Nij are the corresponding observed statistics produced by the adult k. 3. Kill the 50 lowest quality adults. Pair off the remaining 50 (to get 25 pairs), and mate each pair four times, to get four children. Randomly alter a small percentage of the children. Call the 100 children “adults”, and proceed to step 2. Variations: Q(k), 100, 50, mating process, random alteration. April 6, 2005 copyright Kevin O'Bryant

The Two Uses of Frequency Analysis We use frequency analysis for two things figure out cryptograms fast automatic language recognition April 6, 2005 copyright Kevin O'Bryant

copyright Kevin O'Bryant Three ciphers Call the message m0, m1, m2, … Caesar ci = mi + k mod 26 Monoalphabetic ci = (mi) In both, the letter “e” is encrypted the same way throughout the message. Vigenère ci = mi + ki mod L mod 26 The key is a string of L numbers k0, k1, …, kL-1. April 6, 2005 copyright Kevin O'Bryant

copyright Kevin O'Bryant Example Let’s encrypt “attack at dawn” using keyword “usa”. Message a t c k d w n Code 19 2 10 3 22 13 key 20 18 sum 11 14 cipher text U L T K D O N Note that both “a” and “c” get encrypted to “U”. Sometimes “t” is encrypted to “L”, and sometimes to “T”. April 6, 2005 copyright Kevin O'Bryant

Vigenère’s Cryptosystem Let’s encrypt the plaintext “prince is my favorite musician” with the keyword “GUITAR”. Step 1: strip formatting: “prince ismyfa vorite musici an” using blocks the same length as our keyword. Step 2: encrypt the first letter of each block with the Caeser-cipher that sends “a” to “G”, the second with that C- c that sends “a” to “U”, the third with that C-c that sends “a” to “I”, the fourth by sending “a” to “T”, fifth by sending “a” to “A”, the sixth by sending “a” to “R”. VLQGCV OMURFR BIZBTV SOABCZ GH Step 3: reformat into a (possibly) different block length. VLQG CVOM URFR BIZB TVSO ABCZ GH April 6, 2005 copyright Kevin O'Bryant

Vigenère’s Cryptosystem History Idea of entertwining two keys came from Leon Battista Alberti around 1465 in Florence Developed by Johannes Trithemius Giovanni Porta Blaise de Vigenère April 6, 2005 copyright Kevin O'Bryant

The Alpha and the Omega of Vigenère’s cryptosystem April 6, 2005 copyright Kevin O'Bryant

Vigenère’s Cryptosystem History Idea of entertwining two keys came from Leon Battista Alberti around 1465 in Florence Developed by Johannes Trithemius Giovanni Porta Blaise de Vigenère Broken by Charles Babbage Publicly broken by Friedrich Kasiski April 6, 2005 copyright Kevin O'Bryant

The Vision of Sin (excerpt) Sit thee down, and have no shame, Cheek by jowl, and knee by knee: What care I for any name? What for order or degree? Let me screw thee up a peg: Let me loose thy tongue with wine: Callest thou that thing a leg? Which is thinnest? Thine or mine? Thou shalt not be saved by works: Thou has been a sinner too: Ruined trunks on withered forks, Empty scarecrows, I and you! Fill the cup, and fill the can: Have a rouse before the morn: Every moment dies a man, Every moment one is born. Alfred Tennyson Image taken from http://charon.sfsu.edu/TENNYSON/tennyson.html April 6, 2005 copyright Kevin O'Bryant

copyright Kevin O'Bryant Babbage to Tennyson [suggested correction to “otherwise beautiful” poem] It must be manifest that if this were true, the population of the world would be at a standstill . . . I would suggest that in the next edition of your poem you have it read – “Every moment dies a man, Every moment 1 1/16 is born.” The actual figure is so long I cannot get it onto a line, but I believe the figure 1 1/16 will be sufficiently accurate for poetry. April 6, 2005 copyright Kevin O'Bryant

Vigenère’s Cryptosystem Strengths Infinite number of keywords Averages frequencies Easy to remember key Considered unbreakable in Black chambers for 200 years Weaknesses Can perform frequency analysis if we know-or guess-the length of the keyword April 6, 2005 copyright Kevin O'Bryant

copyright Kevin O'Bryant Applets There are applets on our website http://www.math.ucsd.edu/~crypto There are applets for encrypting, decrypting, and breaking: Monoalphabetic Vigenere (Caesar is special case) Rectangular Transposition The “computer homework” mentioned in the introduction of the class will consist of breaking three ciphertexts (each person gets their own) using the applets. The results will be automatically recorded! You can use the applets for practice, but the homework isn’t set up yet. Patience is a virtue. April 6, 2005 copyright Kevin O'Bryant