Ch3 Cryptanalysis for Classical Crypto

8/16/2019 Ch3 Cryptanalysis for Classical Crypto

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CryptanalysisFor Classical cryptography


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Cryptanalysis: Monoalphabetic/polyalphabetic


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Problem of Substitutions

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Each plaintext letter is mapped to exactly one ciphertextletter

=> letter frequency is always applicable


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Substitutions are Monoalphabetic

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Shift (Ceaser) Cipher can be viewed as: For key 17 = R:

R R R R R R

A T T A C K

R K K R T B


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Substitutions are Monoalphabetic

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Shift (Ceaser) Cipher can be viewed as: For key 17 = R:

R R R R R R

A T T A C K

R K K R T B


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Polyalphabetic

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Chose a key with multiple letters, i.e. multiple-keys foreach letter substitution:

S E C U R E

A T T A C K

S X V C T O

Note: each occurrence of A and T is encrypted differently!


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Polyalphabetic

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To encrypt, use the Vigenère table:


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Polyalphabetic

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Example of T encryption with key E:


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Polyalphabetic

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Our example works fine:

S E C U R E

A T T A C K

S X V C T O

In practice, key is shorter than message:

key: Deceptive plaintext: “We are discovered save yourself”.


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Vigenère Cipher

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This is why we repeat the key:

key: deceptivedeceptivedeceptive

plaintext: wearediscoveredsaveyourself

ciphertext: zicvtwqngrzgvtwavzhcqyglmgj


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Vigenère Cipher

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Plaintext letters: P = p0, p1, p2, ..., pn-1

Key letters:

K = k0, k1, k2, ..., km-1 where usually m


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Vigenère Cipher

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General rule: Ci = (pi + ki mod m) mod 26

Decryption:

pi = (Ci - ki mod m) mod 26


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Vigenère Weakness

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Similar plain/cipher letter sequences are encrypted in thesame cipher sequences:

Key: deceptivedeceptivedeceptive

Plaintext: wearediscoveredsaveyourself

Ciphertext: zicvtwqngrzgvtwavzhcqyglmgj


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Vigenère Weakness

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Vigenère Weakness

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Vigenère Weakness

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Plaintext: wearediscoveredsaveyourself Ciphertext: zicvtwqngrzgvtwavzhcqyglmgj

If two identical sequences of plaintext letters occur at adistance that is an integer multiple of the keyword length,they will generate identical ciphertext sequences


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Vigenère Cryptanalysis

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In our example, key length is either 3 or 9:




9


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Note: the appearance of VTW twice could be by chance!

However, if the message is long enough, there will be a

number of such repeated ciphertext sequences.

By looking for common factors in the displacements of

the various sequences, the analyst should be able to make

a good guess of the keyword length


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Example:KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGIL

TXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWC

RXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJ

UWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDIS

PZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNR

WXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVL

NHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST


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Positions: 108, 126, 264, 318, and 330

Key length m is most likely = gcd(δ1, δ2, …)


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Remedy

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The absolute remedy of this weakness is to use a key as

long as the message

It produces random output that bears no statistical

relationship to the plaintext

It is simply unbreakable!


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Example

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Example:

Ciphertext:

ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYTS

Key:

pxlmvmsydofuyrvzwc tnlebnecvgdupahfzzlmnyih

Plaintext:

mr mustard with the candlestick in the hall

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Ch3 Cryptanalysis for Classical Crypto