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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

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cryptanalysis

Cryptanalysis

Kyle Johnson

cryptology
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 access to the contents of encrypted messages or obtaining the key itself.
history
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
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

http://en.wikipedia.org/wiki/File:Vigen%C3%A8re_square_shading.svg

classical ciphers
Classical Ciphers
  • Term given by William Friedman in 1920
  • First recorded explanation in the 9th century by Al-Kindi
    • A manuscript
  • Blaise de Vigenereused a repeating key cipher
significance in history
Significance in History
  • Mary, Queen of Scots
  • World War I, Zimmerman Telegram
  • World War II, German Enigma Machine
cryptanalysis results breaks
Cryptanalysis Results (Breaks)
  • Total Break
  • Global deduction
  • Instance (local) deduction
  • Information Deduction
  • Distinguishing algorithm
types of attacks
Types of Attacks
  • Ciphertext-only
  • Known-plaintext
  • Chosen-plaintext
  • Chosen-Ciphertext
ciphertext only
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
Known-plaintext
  • Attacker has both the plaintext and ciphertext.
  • Goal: get the key
  • WWII: German Enigma Machine
  • Length, patterns, frequency
known plaintext example
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
Chosen-Plaintext
  • Choose Plaintext to get random ciphertext
  • Goal: Weaken the security, get key
  • Plaintext injections
  • Types of chosen-plaintext
    • Batch chosen-plaintext
    • Adaptive chosen-plaintext
batch chosen plaintext attack
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.
adaptive chosen plaintext attack
Adaptive Chosen-plaintext Attack
  • Attacker will make a series of interactive queries
  • Choosing subsequent plaintexts based on the information from the previous encryptions
chosen ciphertext
Chosen Ciphertext
  • Choose ciphertext, decrypt unknown key
  • Enter multiple ciphertexts
  • May be both adaptive and non-adaptive
  • Types of chosen-ciphertext
    • Lunchtime Attack
    • Adaptive 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.
adaptive chosen ciphertext
Adaptive chosen-ciphertext
  • 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
Tests and Analysis
  • Frequency Analysis
  • Index of Coincidence
  • Kasiski Test
frequency analysis
Frequency Analysis
  • Frequency of letters
  • Used to solve classical ciphers
    • Substitution
    • Caesar
  • Natural Langauge properties and patterns
example of frequency analysis
Example of Frequency Analysis
  • Consider this ciphertext :
  • “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
example of frequency analysis1
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 analysis2
Example of Frequency Analysis
  • “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
example of frequency analysis3
Example of Frequency Analysis

“XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”

example of frequency analysis4
Example of Frequency Analysis

“XEJE WI RN EDCQLSE MO R OJEKGENYB RNRSBIWI”

example of frequency analysis5
Example of Frequency Analysis

Decrypted: “HERE IS AN EXAMPLE OF A FREQUENCY ANALYSIS”

Encrypted: “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”

kasiski test
Kasiski Test
  • Method of attacking polyalphabetic substitution ciphers
  • Deduce length of Keyword
  • ‘m’ number of rows
  • Identical Segments of Ciphertext, length >= 3
kasiski test1
Kasiski Test
  • Consider the following text:
  • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
kasiski test2
Kasiski Test
  • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
  • Trigram HJV
kasiski test3
Kasiski Test
  • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
  • Trigram HJV : differences (δ) = 18, 138, 54, 12
kasiski test4
Kasiski Test
  • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
  • Trigram HJV : differences (δ) = 18, 138, 54, 12
  • Greatest common denominator: m = 6 , length of the keyword is 6.
index of coincidence
Index of Coincidence
  • Comparing 2 partials of same ciphertext
  • Ciphertext coincidences same in Plain Text
  • Used to help solve Vigenerecipher.
  • Check if two texts are in the same language, dialect
index of coincidence1
Index of Coincidence
  • Consider the text from the Kasiski Test:
  • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
  • And the length of the keyword m = 6
index of coincidence2
Index of Coincidence
  • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
  • 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 coincidence3
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
  • =
smaller example ioc
Smaller example: IoC
  • Consider x = “abaaabcda”
  • So as you can see there are 5:a, 2:b, 1:c, 1:d, 9 in total
  • =
smaller example ioc1
Smaller example: IoC
  • Consider x = “abaaabcda”
  • So as you can see there are 5:a, 2:b, 1:c, 1:d, 9 in total
  • =
  • Using the above equation we find that
  • = =
index of coincidence4
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
Other attacks
  • Brute-Force Attack
  • Boomerang Attack
  • Linear cryptanalysis
  • Brute-Force Attack
  • Boomerang Attack
  • Linear cryptanalysis
attack runtimes
Attack runtimes
  • Brute-Force with permutations per second
  • bits takes < 1 nanosecond
  • bits takes ~4.25 minutes
  • bits takes ~150 trillion years
  • bits takes ~ years
today s cryptanalysis
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
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