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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

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

10. 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

11. 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
April 6, 2005
copyright Kevin O'Bryant

12. 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

13. 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

14. copyright Kevin O'Bryant
Applets
There are applets on our website
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