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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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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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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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Similar plain/cipher letter sequences are encrypted in thesame cipher sequences:
Key: deceptivedeceptivedeceptive
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:
Key: deceptivedeceptivedeceptive
Plaintext: wearediscoveredsaveyourself
Ciphertext: zicvtwqngrzgvtwavzhcqyglmgj
9
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Vigenère Cryptanalysis
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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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Vigenère Cryptanalysis
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Example:KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGIL
TXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWC
RXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJ
UWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDIS
PZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNR
WXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVL
NHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
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Vigenère Cryptanalysis
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Example:KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGIL
TXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWC
RXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJ
UWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDIS
PZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNR
WXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVL
NHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
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Vigenère Cryptanalysis
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Example:KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGIL
TXRGUDDKOTFMBPVGEGLTGCKQRACQCWDNAWC
RXIZAKFTLEWRPTYCQKYVXCHKFTPONCQQRHJVAJ
UWETMCMSPKQDYHJVDAHCTRLSVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMVGKMITZHFPDIS
PZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFSPEZQNR
WXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVL
NHIFFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIYCWHJVLNHIQIBTKHJVNPIST
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