Crypto for CTFs
RPISEC 2013
Ben Kaiser
Terminology
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plaintext - the original message
ciphertext - the coded message
cipher - algorithm for transforming plaintext to ciphertext
key - info used in cipher known only to sender/receiver
encipher (encrypt) - converting plaintext to ciphertext
decipher (decrypt) - recovering ciphertext from plaintext
cryptography - study of encryption principles/methods
cryptanalysis (codebreaking) - the study of principles/methods
of deciphering ciphertext without knowing key
Classification
• Characterize by:
• Type of encryption operations used
• substitution
• transposition
• product
• Number of keys used
• single-key (private)
• two-key (public)
• Way in which plaintext is processed
• Block – processes a block of element at a time
• Stream – processes continuous stream of elements
Classical Ciphers - Substitution
• Letters of plaintext are replaced by other letters or by
numbers or symbols.
• Monoalphabetic ciphers: For every letter, one and only one
letter (or symbol) is substituted.
• Polyalphabetic ciphers: Throughout the cipher text, different
symbols can stand for the same letter, and the same symbols
can stand for different letters
Monoalphabetic Ciphers
The “key” for substitution ciphers is a mapping from plaintext
alphabet to ciphertext alphabet. It must be known to both
parties.
• Caesar cipher:
• Each character is converted to a numeric value (0-25), then
summed with a constant value (the key) and modded by 25.
• rpisecisfun becomes uslvhflvixq if the key is 3.
Monoalphabetic Ciphers
• The Caesar Cipher is easy to break by brute force since there
are only 25 possible keys. Let’s look at a more complex
monoalphabetic cipher.
• What if we had a 26-character key that maps each plaintext
character to a ciphertext character at random? That gives 26!
= 403 septillion possible keys.
Frequency Analysis
• You’d think this would be incredibly difficult to break, but it’s
not thanks to frequency analysis
• In English, “E” is the most common letter, followed by
T,R,N,I,O,A, and S. Z,J,K,Q, and X are quite rare.
Frequency Analysis
• Calculate the letter frequencies for your ciphertext, then
compare counts against known values.
• Use known tricks:
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The most common letter at the end of a word is E
The most common beginning letter of a word is T
A single-letter word is A or I, and on rare occasions, O.
The most frequent two-letter word is OF, followed by TO and IN
The most used three-letter word is THE, next common is AND
The most frequent four-letter word is THAT
Q is always followed by U
The most common double letters are: LL, EE, SS, OO, TT, FF, RR,
NN, PP and CC
Practice: Cracking a
Monoalphabetic Cipher
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZV
UEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPD
ZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Hints:
Practice: Cracking a
Monoalphabetic Cipher
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZV
UEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPD
ZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Hints:
• Count the letter frequencies and compare to the chart. Make
educated guesses and work from there (guess & check).
Practice: Cracking a
Monoalphabetic Cipher
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZV
UEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPD
ZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Hints:
• Count the letter frequencies and compare to the chart. Make
educated guesses and work from there (guess & check).
• P & Z are very frequent in the ciphertext – let’s guess those are E
and T, the two most common letters in English.
Practice: Cracking a
Monoalphabetic Cipher
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZV
UEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPD
ZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Hints:
• Count the letter frequencies and compare to the chart. Make
educated guesses and work from there (guess & check).
• P & Z are very frequent in the ciphertext – let’s guess those are E
and T, the two most common letters in English.
• ZW is a common letter combination. If Z = T then maybe TH?
What does that make ZWP likely to be?
Practice: Cracking a
Monoalphabetic Cipher
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZV
UEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPD
ZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Hints:
• Count the letter frequencies and compare to the chart. Make
educated guesses and work from there (guess & check).
• P & Z are very frequent in the ciphertext – let’s guess those are E
and T, the two most common letters in English.
• ZW is a common letter combination. If Z = T then maybe TH?
What does that make ZWP likely to be?
• “It was disclosed yesterday that several informal but direct
contacts have been made with political representatives of the
vietcong in moscow.”
CSAW 2011 Crypto5: 200 Pts
JR UNIR QVFPBIRERQ GUNG BHE YNFG GUERR GENAFZVFFVBAF
JR'ER RNFVYL QRPVCURERQ. JR UNIR GNXRA PNER BS GUR
CNEGL ERFCBAFVOYR SBE GURVE RAPBQVAT NAQ NER ABJ
HFVAT N ARJ ZRGUBQ. HFR GUR VASBEZNGVBA CEBIVQRQ NG
YNFG JRRX.F ZRRGVAT GB QRPVCURE NYY ARJ ZRFFNTRF. NAQ
ERZRZORE, GUVF JRRX.F XRL VF BOSHFPNGRQ.
No hint was provided, but I’ve only showed you one cipher so
far so connect the dots.
CSAW 2011 Crypto5: 200 Pts
JR UNIR QVFPBIRERQ GUNG BHE YNFG GUERR GENAFZVFFVBAF
JR'ER RNFVYL QRPVCURERQ. JR UNIR GNXRA PNER BS GUR
CNEGL ERFCBAFVOYR SBE GURVE RAPBQVAT NAQ NER ABJ
HFVAT N ARJ ZRGUBQ. HFR GUR VASBEZNGVBA CEBIVQRQ NG
YNFG JRRX.F ZRRGVAT GB QRPVCURE NYY ARJ ZRFFNTRF. NAQ
ERZRZORE, GUVF JRRX.F XRL VF BOSHFPNGRQ.
Answer: The key is 13.
WE HAVE DISCOVERED THAT OUR LAST THREE TRANSMISSIONS
WERE EASILY DECIPHERED. …
PHDays CTF 2013: Crypto 100
Decrypt the message:
7y9rr177sluqv1r4pw
Hint: at $
PHDays CTF 2013: Crypto 100
Decrypt the message:
7y9rr177sluqv1r4pw
Hint: at $
The cipher used is the Atbash Cipher. Each letter is assigned to
the letter at the opposite end of the alphabet – A=Z, B=Y, C=X,
etc. In this case, the numbers 0-9 were added onto the end of the
key so A=9, B=8, … J=1, K=Z, L=Y, etc.
PHDays CTF 2013: Crypto 100
Decrypt the message:
7y9rr177sluqv1r4pw
Hint: at $
The cipher used is the Atbash Cipher. Each letter is assigned to
the letter at the opposite end of the alphabet – A=Z, B=Y, C=X,
etc. In this case, the numbers 0-9 were added onto the end of the
key so A=9, B=8, … J=1, K=Z, L=Y, etc.
classiccryptoisfun
CSAW 2011 Crypto1 – 100 pts
87 101 108 99 111 109 101 32 116 111 32 116 104 101 32 50 48
49 49 32 78 89 85 32 80 111 108 121 32 67 83 65 87 32 67 84 70
32 101 118 101 110 116 46 32 87 101 32 104 97 118 101 32 112
108 97 110 110 101 100 32 109 97 110 121 32 99 104 97 108
108 101 110 103 101 115 32 102 111 114 32 121 111 117 32 97
110 100 32 119 101 32 104 111 112 101 32 121 111 117 32 104
97 118 101 32 102 117 110 32 115 111 108 118 105 110 103 32
116 104 101 109 32 97 108 108 46 32 84 104 101 32 107 101
121 32 102 111 114 32 116 104 105 115 32 99 104 97 108 108
101 110 103 101 32 105 115 32 99 114 121 112 116 111 103 114
97 112 104 121 46
This is a simple monoalphabetic cipher. Do these numbers look
like anything you recognize? If not, try frequency analysis.
More Advanced
Monoalphabetic Ciphers
• The Playfair Cipher is a famous advanced Monoalphabetic
Cipher that uses single word as a key. That word is used to
generate a 5x5 character matrix:
• If “MONARCHY” is the key, our matrix looks like this:
MONAR
CHYBD
EFGIK
LPQST
UVWXZ
Playfair Cipher
• plaintext encrypted two letters at a time:
• if a pair is a repeated letter, insert a filler like 'X', eg. "balloon"
encrypts as "ba lx lo on"
• if both letters fall in the same row, replace each with letter to
right (wrapping back to start from end), eg. “ar" encrypts as
"RM"
• if both letters fall in the same column, replace each with the
letter below it (again wrapping to top from bottom), eg. “mu"
encrypts to "CM"
• otherwise each letter is replaced by the one in its row in the
column of the other letter of the pair, eg. “hs" encrypts to "BP",
and “ea" to "IM" or "JM" (as desired)
• Decrypt ONANMSVFBIKLEBUBFSCFAT using “MONARCHY” as
a key.
Polyalphabetic Ciphers
• In a polyalphabetic ciphers, each letter of a ciphertext does
not always decrypt to the same plaintext letter.
• The Vigenère Cipher is essentially multiple Caesar Ciphers:
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key is multiple letters long K = k1 k2 ... kd
ith letter specifies ith alphabet to use
use each alphabet in turn
repeat from start after d letters in message
Vigenère Cipher
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write the plaintext out
write the keyword repeated above it
use each key letter as a caesar cipher key
encrypt the corresponding plaintext letter
eg using keyword deceptive
• key:
• plaintext:
• ciphertext:
deceptivedeceptivedeceptive
wearediscoveredsaveyourself
ZICVTWQNGRZGVTWAVZHCQYGLMGJ
Kasiski Method of Breaking
Vigenère
• Guess the key length
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Find a number of duplicated sequences
Collect all their distances apart
Look for common factors
Thus obtain a set of monoalphabetic ciphers (each is subject to letter
fq. Char.)
repetitions in ciphertext give clues to period
so find same plaintext an exact period apart
which results in the same ciphertext
of course, could also be random fluke
eg repeated “VTW” in previous example
• suggests size of 3 or 9
• then attack each monoalphabetic cipher individually using same
techniques as before
Transposition Ciphers
• Transposition (or permutation) ciphers hide the message by
rearranging the letter order in the message without altering
the actual letters used.
• The classic example is the Rail Fence cipher, in which you write
message letters out diagonally over a number of rows, then
read off the cipher row by row.
• Plain Text: Meet me tonight + padding(qxz)
M E M T N G T X
E T E O I H Q Z
• Cipher Text: MEMTNGTXETEOIHQZ