1. Cryptography Kevin O’Bryant kobryant@ucsd.edu
Math 187
MWF 12:00 – 12:50 pm

2. What is Cryptography?
The art of hiding in plain sight
This line of the presentation is not encrypted.
hTsi ilen fo htp eerestntaoii ne scryrtpde.

Uijt mjof pg uif qsftfoubujpo jt fodszqufe.

3. Steganography
Hidden writing (or writing with a hidden message)
If I u s e a l o n g e n o u g h s e n t e n c e , t h e n I c a n s e n d y o u a q u ic k s h o rt m e s s a g e i n si d e t h e s e n t e n c e b y w ri ti n g t h e l e tt e r s i n t w o d if f e r e n t t y p e f a c e s .
JSteg
Head tattoos
H is t a i a e u s , a c c o r d i n g t o H e r o d o t u s

4. Strangecosmos.com

5. Steganography
Steganography means “hidden writing”
Head tattoos
Microdots
Invisible Ink
Hungarian vowels
Not what we will study

6. Other Ways of Securing Info
Locks
T h i n g s y o u h a v e
T h i n g s y o u k n o w
T h i n g s y o u a r e
Foreign Languages
Codes: “The Eagle has Landed”

7. Plaintext : abcdefghijklmnopqrstuvwxyz
Cryptograms
A cryptogram is when you take a message, and replace each letter with some other letter.
Plaintext : abcdefghijklmnopqrstuvwxyz
Ciphertext: DEFGHIJKLMNOPQRSTUVWXYZABC
“a lp h a b et s o u p”  “ D O S K D E H W V R X S ”
Things to note:
Pl ai nt e xt is in lo w er c a s e, ci p h er te xt is in u p p er c a s e
If w e e n c o u nt er “ D O S K D E H W ”, w e k n o w th at it is a n 8 le tt er w or d w h o s e fir st a n d fif th le tt er s ar e th e s a m e.
P u n ct u at io n (i n cl u di n g s p a c e s) is of te n le ft al o n e.
T h e ci p h er te xt al p h a b et d o e s n ot h a v e to b e “i n or d er ”

8. From www.geocities.com/cryptogramcorner/
M BZHS UDJU SDOZ UDMZEV FHZ'U EH SOKK UDOQ KMBO UH GKJAO UDO YWOVMFOZUV, JZF UDJU MV HZO HL UDO UDMZEV SDMND YWOVMFOZUV JWO YJMF LHW. CHDZ L. BOZZOFQ
From
What stands out about this text?
The apostrophe (preceded by “n”, followed by “t”)
A one letter word (either “i” or “a”)
The last line looks like a name.
Ciphertext: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Plaintext : ____________i_______t____n

9. From www.geocities.com/cryptogramcorner/
i BnHS tDJt SDOn tDinEV FHn‘t EH SOKK tDOQ KiBO tH GKJAO tDO YWOViFOntV, JZF tDJt MV HnO HL tDO tDinEV SDiND YWOViFOntV JWO YJiF LHW. CHDn L. BOnnOFQ
From
Ciphertext: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Plaintext : ____________i_______t____n
There are several “t” followed by “D”, including “tDJt” and “tDO” (twice each). Guess: “tDO” is “the”, and “tDJt” is “that”. Note the “J”=“a” is consistent with the guess that the first word is “i” rather than “a”.

10. From www.geocities.com/cryptogramcorner/
i BnHS that SDen thinEV FHn‘t EH SeKK theQ KiBO tH GKaAe the YWeViFentV, aZF that MV Hne HL the thinEV ShiNh YWeViFentV aWe YaiF LHW. CHhn L. BenneFQ
From
Ciphertext: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Plaintext : ___h_____a__i_e_____t____n
The first name ends in __hn. There aren’t many like that, but there is one common name.
Let’s switch to a Java applet for the sake of speed.

11. Make obvious substitutions, and see if they lead you to guess more.
Solving Cryptograms
Look at the text: are there punctuation, formatting, or other clues apparent?
Make obvious substitutions, and see if they lead you to guess more.
Iterate
More an art than a science
It takes quite some time to become fast at solving cryptograms, and this is not the purpose of this course

12. Cryptanalysis There are tools to help!
Here is a chart of the frequency of letter usage in the Declaration of Independence (6605 letters), the Gettysburg Address (1001 letters), and President Bush’s 2003 State of the Union speech (25169 letters)

13. The most frequent letters in (Bush’s) English are:
Letter Frequencies
The most frequent letters in (Bush’s) English are:
eat on irs
6.7 s
7.0% r
7.2% i
7.4% n
7.7% o
8.3% t
8.7% a
12% e

14. The least frequent letters in (Bush’s) English are: 0.99% v 0.61% k
Letter Frequencies
The least frequent letters in (Bush’s) English are:
0.99% v
0.61% k
0.20% x
0.16% q
0.15% j
0.068 z

15. Page of “A Manuscript on Deciphering Cryptographic Messages”, a book of Abū Yūsūf Ya’qūb ibn Is-hāq ibn as-Sabbāh ibn `omrān ibn Ismaīl al-Kindī, ninth-century scientist.
This image is taken from “The Code Book”, by Simon Singh, who credits Ibrahim A. al-Kadi and Mohammed Mrayati, King Saud University, Riyadh.

16. Who are the teaching assistants?
Class Structure
Who is the professor?
K e vi n O ’B ry a nt ?
Who are the teaching assistants?
G re g g M u si k er
B ar ry S m it h
L ei W u
Where is the class website?
ht tp :// w w w . m at h. u c s d. e d u/ ~ cr y pt o
P a s s w or d pr ot e ct e d

17. Class Structure What is the textbook? Attendance Graded Things
In cr e at io n
Attendance
re q ui re d
Graded Things
5 e x a m s (n ot th e fir st w e e k)
Fi n al e x a m h a s v al u e of 3 q ui z z e s
C u m u l a t i v e , F r i d a y 1 1 : : 3 0
M u st u s e cr y pt o gr a p h y s of tw ar e (1 q ui z)
C h all e n g e p oi nt s sc at te re d ar o u n d
Office Hours
B y a p p oi nt m e nt
L u n c h

18. We will focus on the math involved in cryptology, specifically
Summary
There’s a lot to information security. Cryptology is the study of rearranging and transposing text, and how to undo rearrangements and transpositions.
We will focus on the math involved in cryptology, specifically
P r o b a b ili t y T h e o r y
I n f o r m a ti o n T h e o r y
N u m b e r T h e o r y