1. An Introduction to Cryptography
CS 41 GW
Poorvi Vora

2. The Greeks Used a rod with a piece of cloth draped around it.
Could be decrypted by draping the cloth around a rod of the same size. Other size rods could not be used.
The rod was the key to the cipher
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3. The Caesar Cipher A B C D E D E F G H ….
Easily decrypted, key is fixed. Even with varying key is easily decrypted.
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4. Substitution cipher
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
C J M Z U V Y W RDBU N J O X A E S L P T F G H I
A letter goes to another one.
Each time a letter appears in the message it encrypts to the same letter in the ciphertext
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5. Substitution cipher – encrypted message
vqwfcqaorqdrwfrfsfeojgjolkqsvirwgicfrquqnbibrwqbwqqjaxslqomuqnbfbiaykqxbqjwfbrobrojqfadrfzuvirwgxlkizuqnboaknrvouqnbfjqaqqdqdgqjxbqjoaqgxlkizfadoaqgjicfrqkqrxbbqqvwfrdimmejqazqrwibsfuqbiarwqaxslqjomuqnbaqqdqd
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6. Frequency of occurence
Ciphertext
q 37
b 16
r 16
f 14
a 13
i 11
j 11
o 11
w 10
d 8
x 7
u 7
n 6
English (every 1000)
E 127
T 91
A 82
O 75
I 70
N 67
S 63
H 61
R 60
D 43
L 40
C 28
k 6
g 6
l 5
s 5
v 5
m 4
z 4
c 3
e 2
y 1
h 0
t 0
p 0
U 28
M 24
W 23
F 22
G 20
Y 20
P 19
B 15
V 10
K 8
J 2
Q 1
X 1
Z 1
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7. Digram/Trigram occurenceTH HE IN ER AN RE ED ON ES ST EN AT
Trigram
THE
ING
AND
HER
ERE
ENT
THA
NTH
WAS
ETH
FOR
DTH TO NT HA ND OU EA NG AS OR TI IS ET IT AR TE SE HI OF
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8. Decrypted plaintext
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z R
F L Z D Q M Y W I E U K S A O G T J B R X C V H N P J
WE HAVE NOTED THAT A MAJOR PROBLEM WITH PRIVATE KEYS IS THE SHEER NUMBER OF KEYS A SINGLE USER HAS TO STORE AND TRACK. WITH PUBLIC KEYS ONLY TWO KEYS ARE NEEDED PER USER ONE PUBLIC AND ONE PRIVATE. LET US SEE WHAT DIFFERENCE THIS MAKES IN THE NUMBER OF KEYS NEEDED.
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9. Vernam Cipher Used by English in WWII
ESCAPE BY THE ROUTE THROUGH BELGRADE
bababl ac ksh eepha veyouan ywoolyes
FSDAQP BA DX…….
Replaced by pieces of silk hidden in socks. Burnt after use.
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10. Modern Cryptography
Need to design ciphers so that breaking is hard even for the computer
Require Mathematics, Algorithms, and Theory of Complexity
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11. The problems modern crypto addresses
Confidentiality/secrecy/privacy
How to keep a message secret so it can be read only by a chosen person
Integrity
How to determine a string of symbols has not been changed since it was created, and that it originated from a particular entity
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12. Research Topics

13. Digital Media

14. Application: Robust, imperceptible watermarking Prevention of digital media piracy
Physical media piracy
Quality deterioration with each copy
Distribution visible and expensive, legal enforcement easier
Digital media piracy
Perfect copies
Distribution unsupervised; no clear laws; no means of enforcing them, most important no easy way of locating distribution centers
Current OS and digital copies: Any object that needs a PC for viewing can be copied perfectly through file copies, and imperfectly through screen captures
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15. Copyright protection with a robust, invisible watermark
Owner looks for the watermark - either all over the Internet, or on an individual picture that she suspects was stolen from her.
Original picture to be sold on the Internet contains an invisible mark:
If she finds it with/being sold by an unauthorized person, she could seek legal recourse.
`watermark’ - something that identifies owner or copyright owner
All existing methods can be busted by free software available on the Internet; it is not a preventive measure, it merely aids in finding the culprit after the fact;
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16. Watermark should survive accidental attacks
Original, legal, buyer performs operations on image - sharpening, brightness/colour adjustment, filtering, cropping, resizing, rotation - while retaining perceptual quality of image.
Watermark should survive such operations - called accidental attacks - and should remain invisible; ie.e watermark should be robust
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17. Image quality degrades if watermark removed (intentional attack)
Illegal reseller trys to destroy watermark before reselling. Watermark should damage perceptual quality of image when being removed (detection procedure does not detect the existence of a watermark) or sufficiently altered (the information contained in it is altered sufficiently - identity of owner is changed). Intentional attack.
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18. User without decryption sees garbage
Encapsulated Content: Better Security, More Expensive – Prevents Unauthorized Use
Content encrypted during transmission and in storage on buyer’s local disk
User without decryption sees garbage
aCd9Tof3trefgu
Evariste Galois
aCd9Tof3trefgu
Content decrypted in hardware or software to allow viewing and manipulation. Pay per view possible
Evariste Galois
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19. Classification of Rights Management Systems
Complexity of access specifications
Low
Medium
High
Personal
Family Multimedia Archives
Personal publishing using templates
Personal metadata?
Lessons/hw by students and teachers
Mixed
Wedding videos professionally filmed
Aggregated Personal metadata?
Type of Content
(Read only) Entertainment Magazine subscriptions
Commercial Photography
Publishing Press
Ebooks
Scientific publishing
Commercial
Use password protection
Use secure encapsulation
Use secure encapsulation + watermarking
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21. Was this image changed in any way after it was captured?
Another problem: Authentication of digital media given cheap access to capable processing systems
Was this image changed in any way after it was captured?
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22. Authentication with a fragile, invisible watermark
In a court of law, a judge checks the watermark hidden in the presented image to see if it is associated in the same way with each pixel of the image presented as evidence
Original picture contains an invisible mark inserted at `source’:
If she finds that the hidden watermark is not what it should be for the presented image, the presented image is not authentic and has been changed since it was obtained.
`watermark’ - something that is associated with the value of each pixel of the image
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23. Auctions and Privacy

24. Privacy Cost
When we re-encounter vendors online, they may use information from previous encounters against us
If amazon knows I’m a crypto fan, why not charge me higher for crypto books?
Would I pay higher on average if they knew stuff about me?
If so, would that be an economic value to privacy in commercial interactions?
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25. eBay example Highest Bids for Auction of Annexation Drone
Bid Order
eBay Identity
Bid Value b1
erelfir
13.50 b2
les-letwin
13.00 b3
daredevilgo
5.55 b4
jan1923
5.09
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26. eBay example Highest Bids for Auction of Annexation Drone
Bid Order
eBay Identity
Bid Value
Price Non-strategic b1
erelfir
13.50 b2
les-letwin
13.00 b3
daredevilgo
5.55 b4
jan1923
5.09 -
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27. eBay example Highest Bids for Auction of Annexation Drone
Bid Order
eBay Identity
Bid Value
Price Non-strategic
Price
Auctions b1
erelfir
13.50 b2
les-letwin
13.00
5.60 b3
daredevilgo
5.55
5.09 b4
jan1923 -
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28. eBay example Highest Bids for Auction of Annexation Drone
Bid Order
eBay Identity
Bid Value
Price Non-strategic
Price
Auctions
Strategic b1
erelfir
13.50
5.12 b2
les-letwin
13.00
5.60
5.11 b3
daredevilgo
5.55
5.09
5.10 b4
jan1923 -
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29. Electronic Voting

30. Receipts for secure transactions
You get a receipt when you use the ATM
You can check your bank statement to ensure the transaction was recorded correctly
Why don’t you get a receipt when you vote, so you can check your vote was correctly counted?
You could use the receipt to sell your vote
The mafia could force you to prove you voted a certain way
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31. Integrity during ballot casting: paper receipts
Challenge: allow the voter to keep a record of her vote so
she can determine that it has been counted correctly, yet
not prove how she voted
This record on paper, so “computer” problems will not destroy the record
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32. The receipt can be encrypted
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33. Key
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34. Overlaid
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35. Voter chooses
The voter chooses one of the two layers shown and takes it home
All encrypted receipts are displayed on the Web
Voter checks to see her receipt is there.
Equivalent to checking her receipt is in the ballot box before counting starts.
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36. Counting
The encrypted votes are passed to several trustees (such as representatives of the candidates, the Electronic Frontier Foundation, a government representative, etc.)
Each trustee does a partial decryption and shuffles the receipts
Finally, decrypted receipts (i.e. votes) are counted.
Trustees can be audited
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37. GW implementation Several
A recent implementation by GW grad student Stefan Popoveniuc and students from UMBC and Univ. of Ottawa won the Student Voting System competition and has been used for student government elections at Univ. of Ottawa
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