Implementing-cryptography-using-python

50 Chapter 2 ■ Cryptographic Protocols and Perfect Secrecy
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Known-Plaintext (KPA) is used when the malicious user has access to
both the plaintext and its encrypted version (ciphertext). Historical ciphers
were very susceptible to this type of attack.
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Chosen-Plaintext (CPA) is an attack that occurs when the malicious users
are able to define their own plaintext and have it encrypted, resulting in
ciphertext that can be analyzed to determine how to decrypt other messages.
A good example is the attacks on the German Enigma machine;
once the Allies captured an Enigma machine, the CPA was used to determine
how the encryption scheme worked.
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Chosen-Ciphertext (CCA) is an attack used where the cryptanalyst can
gather information by obtaining the decryptions of chosen ciphertexts.
One way to think about this type of attack is that you can test a slightly
adjusted encryption. Change a bit and see if the decrypted message turns
to gibberish. For instance, if you are a server on the internet and you
change an encrypted packet in some way, you can see how the target
reacts to your change when they go to decrypt.
Shannon’s Theorem
Claude Shannon (1916–2001) was often regarded as the father of modern cryptology
and information theory. After receiving his Ph.D. in mathematics, Shannon
contributed to the field of cryptanalysis for national defense during World War
II. He is also credited for the founding of digital circuit design theory in 1937.
He published a paper in 1949 entitled “Communication Theory and Secrecy
Systems.” In this revolutionary paper, Shannon defines perfect secrecy for
secret-key systems and shows that they exist. A secret-key cipher obtains perfect
secrecy if for all plaintexts x and all ciphertexts y, it holds that Pr(x) = Pr(x|y). In
other words, a ciphertext y gives no information about the plaintext. Shannon’s
principle states, “The enemy knows the system.”
Known as the gold standard of security in cryptography, “perfect security”
is a special case of information-theoretic security wherein for an encryption
algorithm, if there is ciphertext produced that uses it, no information about the
message is provided without knowledge of the key. Examine the definition of
perfect security as defined by Shannon.
Let ε = (E,D) be a Shannon cipher defined over (K,M,C). Consider a probabilistic
experiment in which the random variable k is uniformly distributed over
K. If for all m 0 , m 1 ∈ M, and all c ∈ C, we have: Pr[E(k, m 0 ) = c] = Pr[E(k, m 1 ) = c];
then we say that ε is a perfectly secure Shannon cipher.
To explain the definition in words, if the probability that a ciphertext c is m 0 is
the same as the probability that the same ciphertext c is m 1 , then the cipher ε is