#### Transcript Cryptanalysis

```Kyle Johnson
Cryptology
 Comprised of both Cryptography and Cryptanalysis
 Cryptography - which is the practice and study of
techniques for secure communication in the presence
of third parties
 Cryptanalysis - which is the art of
defeating cryptographic security systems, and gaining
obtaining the key itself.
History
• Fialka Cipher machine
• Used by the Soviet in the
cold war era.
• Uses 10 rotors each with 30
contacts and also makes
use of a punch card
mechanism.
http://en.wikipedia.org/wiki/File:FIALKA-rotors-in-machine.jpg
Cryptanalysis Tools
Scytale(rhymes with Italy)
Ancient Greek device used to
implement a cipher.
Vigenere square used for the Vigenere
Cipher.
http://www.braingle.com/brainteasers/codes/images/scytale.gif
Classical Ciphers
 Term given by William Friedman in 1920
 First recorded explanation in the 9th century by Al-
Kindi
 A manuscript
 Blaise de Vigenere used a repeating key cipher
Significance in History
 Mary, Queen of Scots
 World War I, Zimmerman Telegram
 World War II, German Enigma Machine
Cryptanalysis Results (Breaks)
 Total Break
 Global deduction
 Instance (local) deduction
 Information Deduction
 Distinguishing algorithm
Types of Attacks
 Ciphertext-only
 Known-plaintext
 Chosen-plaintext
 Chosen-Ciphertext
Ciphertext-only
 Also known as the known-ciphertext attack
 Attacker only has a set of Ciphertexts
 Successful, plaintext or key obtained
 Used in Frequency Analysis
Known-plaintext
 Attacker has both the plaintext and ciphertext.
 Goal: get the key
 WWII: German Enigma Machine
 Length, patterns, frequency
Known-Plaintext Example
 Plaintext: “THIS IS AN EXAMPLE OF A CIPHER”
 Ciphertext: “XLMW MW ER IBEQTPI SJ E GMTLIV”
 Try Caesar Cipher: word length pattern noticed.
 Shift-1 Plaintext: “UIJT JT BO FYBNQMF PG B DJQIFS”
 Ciphertext: “XLMW MW ER IBEQTPI SJ E GMTLIV”
 Not the same. Repeat for all possible shifts(25 times)
 Shift -4 Plaintext: “XLMW MW ER IBEQTPI SJ E GMTLIV”
 Ciphertext: “XLMW MW ER IBEQTPI SJ E GMTLIV”
 Same!
 Caesar cipher: key is shift of 4.
Chosen-Plaintext
 Choose Plaintext to get random ciphertext
 Goal: Weaken the security, get key
 Plaintext injections
 Types of chosen-plaintext
 Batch chosen-plaintext
Batch Chosen-plaintext Attack
 Chooses all of the plaintexts before they are encrypted
 This is the means of an unqualified use of this type of
attack on encrypted data.
 Attacker will make a series of interactive queries
 Choosing subsequent plaintexts based on the
information from the previous encryptions
Chosen Ciphertext
 Choose ciphertext, decrypt unknown key
 Enter multiple ciphertexts
 Types of chosen-ciphertext
 Lunchtime Attack
Lunchtime Attack
 Also known as the midnight or indifferent attack
 Attacker makes adaptive chosen-ciphertext queries up
to a certain point
 Can attack computer while user at lunch.
 Attack in which ciphertexts may be chosen adaptively
and after a challenge ciphertext is given to the attacker
 Ciphertext can’t be used itself
 Stronger attack than lunchtime but few practical
attacks are of this form
Tests and Analysis
 Frequency Analysis
 Index of Coincidence
 Kasiski Test
Frequency Analysis
 Frequency of letters
 Used to solve classical ciphers
 Substitution
 Caesar
 Natural Langauge properties and patterns
Example of Frequency Analysis
 Consider this ciphertext :
 “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
Example of Frequency Analysis
 “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
 A: 0
 B: 2
 C: 1
 So on down the alphabet…
Example of Frequency Analysis
 “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
Frequency
8
6
4
2
0
Freq.
A B C D E F G H I J K L MNO P Q R S T U VWX Y Z
Example of Frequency Analysis
“XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
Frequency
8
6
4
2
0
Freq.
A B C D E F G H I J K L MN O P Q R S T U VWX Y Z
Example of Frequency Analysis
“XEJE WI RN EDCQLSE MO R OJEKGENYB RNRSBIWI”
Frequency
8
6
4
2
0
Freq.
A B C D E F G H I J K L MN O P Q R S T U VWX Y Z
Example of Frequency Analysis
Encrypted: “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
Decrypted: “HERE IS AN EXAMPLE OF A FREQUENCY ANALYSIS”
Frequency
8
6
4
2
0
Freq.
A B C D E F G H I J K L MNO P Q R S T U VWX Y Z
Kasiski Test
 Method of attacking polyalphabetic substitution
ciphers
 Deduce length of Keyword
 ‘m’ number of rows
 Identical Segments of Ciphertext, length >= 3
Kasiski Test
 Consider the following text:
 KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDK
OTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKY
VXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSK
CGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHF
PDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVY
CGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACN
VRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJ
VNPIST
Kasiski Test
 KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDK
OTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKY
VXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSK
CGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHF
PDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVY
CGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACN
VRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJ
VNPIST
 Trigram HJV
Kasiski Test
 KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDK
OTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKY
VXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSK
CGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHF
PDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVY
CGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACN
VRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJ
VNPIST
 Trigram HJV : differences (δ) = 18, 138, 54, 12
Kasiski Test
 KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDK
OTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKY
VXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSK
CGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHF
PDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVY
CGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACN
VRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJ
VNPIST
 Trigram HJV : differences (δ) = 18, 138, 54, 12
 Greatest common denominator: m = 6 , length of the keyword is 6.
Index of Coincidence
 Comparing 2 partials of same ciphertext
 Ciphertext coincidences same in Plain Text
 Used to help solve Vigenere cipher.
 Check if two texts are in the same language, dialect
Index of Coincidence
 Consider the text from the Kasiski Test:
 KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLT
GCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWET
MCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJ
UMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYC
GAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFE
XOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
 And the length of the keyword m = 6
Index of Coincidence
 KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLT
GCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWET
MCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJ
UMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYC
GAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFE
XOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
 And the length of the keyword m = 6
 Index of coincidence requires one to break the ciphertext up into the m number of rows.
Each with as similar number of letters as possible.
Index of Coincidence
 Index of coincidence requires one to break the ciphertext up into the length (m) number
of rows. Each with as similar number of letters as possible.
 y1= KGQNGVGGTGCQWAWQHNJEPJTKQFWAP…
 y2= CUTRRFIUFEKCCKRKKCVTKVRCDRSFR…
 y3= CFYRKDLDMGQWRFPYFQAMQDLGZLJSJ…
 y4= PDATDETDBLRDXTTVTQJCDASCXSTIA…
 Y5= KPVMNTXKPTANILYXPRUMYHVZGWBAH…
 Y6= BHIVBDROVGCAZECCOHWSHCSQSCHSK…
 It comes out to look something like this (not full rows)
 The index of coincidence is denoted as
 𝐼𝐶 𝑥 =
26
𝑖=1
𝑛
2
𝑓𝑖
2
=
#𝑃𝑎𝑖𝑟𝑠 𝑜𝑓 𝑖𝑑𝑒𝑛𝑡𝑖𝑐𝑎𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠
# 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑖𝑟𝑠
Smaller example: IoC
 Consider x = “abaaabcda”
 So as you can see there are 5:a, 2:b, 1:c, 1:d, 9 in total
 𝐼𝐶 𝑥 =
26
𝑖=1
𝑛
2
𝑓𝑖
2
=
#𝑃𝑎𝑖𝑟𝑠 𝑜𝑓 𝑖𝑑𝑒𝑛𝑡𝑖𝑐𝑎𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠
# 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑖𝑟𝑠
Smaller example: IoC
 Consider x = “abaaabcda”
 So as you can see there are 5:a, 2:b, 1:c, 1:d, 9 in total
 𝐼𝐶 𝑥 =
26
𝑖=1
𝑛
2
𝑓𝑖
2
=
#𝑃𝑎𝑖𝑟𝑠 𝑜𝑓 𝑖𝑑𝑒𝑛𝑡𝑖𝑐𝑎𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠
# 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑖𝑟𝑠
 Using the above equation we find that
 𝐼𝐶 𝑥 =
2
5
+
2
2
9
2
=
10+1
36
=
11
36
Index of Coincidence
 For English text the index of coincidences is
approximately .o66
 The index of coincidence for the previous example:







m = 1: 0.041
m = 2: 0.038, 0.047
m = 3: 0.056, 0.048, 0.048
m = 4: 0.037, 0.042, 0.037, 0.050
m = 5: 0.043, 0.043, 0.031, 0.035, 0.043
m = 6: 0.063, 0.084, 0.049, 0.065, 0.042, 0.071
m = 7: 0.031, 0.044, 0.043, 0.038, 0.044, 0.044, 0.041
 Since the values are closest to .066 where m = 6 it is
the appropriate choice for the keyword length.
Other attacks
 Brute-Force Attack
 Boomerang Attack
 Linear cryptanalysis
 Brute-Force Attack
 Boomerang Attack
 Linear cryptanalysis
Attack runtimes
 Brute-Force with 256 permutations per second
 28 bits takes < 1 nanosecond
 264 bits takes ~4.25 minutes
 2128 bits takes ~150 trillion years
 2256 bits takes ~51 × 1051 years
Today’s Cryptanalysis
 The NSA has developed, due to an enormous
breakthrough, the ability to cryptanalyze
unfathomably complex encryption systems
 This includes those developed by other governments
but as well as average computer users in the US
 The NSA is known for its mathematical breakthroughs
in cryptanalysis especially differential cryptanalysis
Questions?
```