Cryptography Reference
In-Depth Information
Note that the encryption by Alice turns the uppercase A into the lower case letter
m . Oscar, the attacker who eavesdrops on the channel, only sees the ciphertext letter
m . Decryption by Bob with the same key stream reproduces the plaintext A again.
So far, stream ciphers look unbelievably easy: One simply takes the plaintext,
performs an XOR operation with the key and obtains the ciphertext. On the receiving
side, Bob does the same. The “only” thing left to discuss is the last question from
above.
What Exactly Is the Nature of the Key Stream?
It turns out that the generation of the values s i , which are called the key stream ,is
the central issue for the security of stream ciphers. In fact, the security of a stream
cipher completely depends on the key stream . The key stream bits s i are not the key
bits themselves. So, how do we get the key stream? Generating the key stream is
pretty much what stream ciphers are about. This is a major topic and is discussed
later in this chapter. However, we can already guess that a central requirement for
the key stream bits should be that they appear like a random sequence to an attacker.
Otherwise, an attacker Oscar could guess the bits and do the decryption by himself.
Hence, we first need to learn more about random numbers.
Historical Remark Stream ciphers were invented in 1917 by Gilbert Vernam, even
though they were not called stream ciphers back at that time. He built an elec-
tromechanical machine which automatically encrypted teletypewriter communica-
tion. The plaintext was fed into the machine as one paper tape, and the key stream
as a second tape. This was the first time that encryption and transmission was au-
tomated in one machine. Vernam studied electrical engineering at Worcester Poly-
technic Institute (WPI) in Massachusetts where, by coincidence, one of the authors
of this topic was a professor in the 1990s. Stream ciphers are sometimes referred to
as Vernam ciphers. Occasionally, one-time pads are also called Vernam ciphers. For
further reading on Vernam's machine, the topic by Kahn [97] is recommended.
2.2 Random Numbers and an Unbreakable Stream Cipher
2.2.1 Random Number Generators
As we saw in the previous section, the actual encryption and decryption of stream
ciphers is extremely simple. The security of stream ciphers hinges entirely on a
“suitable” key stream s 0 , s 1 , s 2 ,... . Since randomness plays a major role, we will first
learn about the three types of random number generators (RNG) that are important
for us.
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