Cryptanalysis
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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


Questions

Questions?


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