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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 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 access to the contents of encrypted messages or 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 http://en.wikipedia.org/wiki/File:Vigen%C3%A8re_square_shading.svg
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 • 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 • Adaptive 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.
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 • 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 • 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 • 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”
Example of Frequency Analysis “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
Example of Frequency Analysis “XEJE WI RN EDCQLSE MO R OJEKGENYB RNRSBIWI”
Example of Frequency Analysis Decrypted: “HERE IS AN EXAMPLE OF A FREQUENCY ANALYSIS” Encrypted: “XZJZ WI RN ZDCQLSZ MO R OJZKGZNYB RNRSBIWI”
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: • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
Kasiski Test • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST • Trigram HJV
Kasiski Test • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST • Trigram HJV : differences (δ) = 18, 138, 54, 12
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 • 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 Coincidence • Consider the text from the Kasiski Test: • KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST • And the length of the keyword m = 6
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 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 • Consider x = “abaaabcda” • So as you can see there are 5:a, 2:b, 1:c, 1:d, 9 in total • =
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 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 permutations per second • bits takes < 1 nanosecond • bits takes ~4.25 minutes • bits takes ~150 trillion years • bits takes ~ 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