Cryptography Introduction, continued. Sufficient key space principle If an encryption scheme has a...
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Transcript of Cryptography Introduction, continued. Sufficient key space principle If an encryption scheme has a...
Sufficient key space principle
• If an encryption scheme has a key space that is too small, then it will be vulnerable to exhaustive-search attacks
The Vigenère cipher
• The key is now a string, not just a character• To encrypt, shift each character in the
plaintext by the amount dictated by the next character of the key– Wrap around in the key as needed
• Decryption just reverses the process
tellhimaboutmecafecafecafecaveqpjiredozxoe
The Vigenère cipher
• Size of key space?– If keys are 14-character strings; then key space
has size 2614 266
– Brute-force search expensive/impossible
• Is the Vigenère cipher secure?
• (Believed secure for many years…)
Attacking the Vigenère cipher
• (Assume a 14-character key)• Observation: every 14th character is
“encrypted” using the same shift
• Looking at every 14th character is(almost) like looking at ciphertextencrypted with the shift cipher– Though brute-force attack from
before doesn’t work…
veqpjiredozxoeualpcmsdjquiqndnossoscdcusoakjqmxpqrhyycjqoqqodhjcciowieii
veqpjiredozxoeualpcmsdjquiqndnossoscdcusoakjqmxpqrhyycjqoqqodhjcciowieii
veqpjiredozxoeualpcmsdjquiqndnossoscdcusoakjqmxpqrhyycjqoqqodhjcciowieii
Using plaintext letter frequencies
8.2
1.5
2.8
4.3
12.7
2.2 2.0
6.1
7.0
0.2 0.8
4.0
2.4
6.7
1.5 1.9
0.1
6.0 6.3
9.1
2.8
1.0
2.4
0.2
2.0
0.1 0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
a b c d e f g h i j k l m n o p q r s t u v w x y z
Perc
enta
ge
Letter
Attacking the Vigenère cipher
• Look at every 14th character of the ciphertext, starting with the first
• Let be the most common character appearing in this portion of the ciphertext
• Most likely, this character corresponds to the most common plaintext character (‘e’)– Guess the first character of the key is - ’e’
• Repeat for all other positions
• Better (more complicated) attacks also possible