Cryptography Reference
In-Depth Information
Exercise 3.4
Prove that reusing keys allows a total break of the one-time pad (which
should not be called that anymore!) under a chosen plaintext attack.
Exercise 3.5
The following is a dialogue extract from the movie 'Swordfish'. The
movie is about a hacker, Stanley, who tries to rescue his daughter and is offered by
Gabriel (a secretive counter-terrorist) the money he needs to do it. But Gabriel wants
him to break a cipher in exchange:
Stanley.-
What kind of cipher?
Gabriel.-
Vernam encryption.
Stanley.-
A Vernam's impossible. Its key code is destroyed upon implementation.
Not to mention being a true 128-bit encryption.
Gabriel.-
Actually, we're talking 512-bit.
Stanley.-
It's impossible.
Gabriel.-
Tell ya what, I'll pay you ten million dollars. That should be enough to
get your daughter back ... unless of course it's impossible.
Stanley.-
Nothing's impossible.
Question:
Comment on this scene from a cryptologic point of view.
Exercise 3.6
The following is a quote from a cryptography text published in 2003:
Concluding Remarks.
If we increase the length of the keyword, then it is more difficult
to break the system. Suppose we want to send a plaintext consisting of 500 letters secretly.
Also we choose a paragraph of a novel, which consists of 500 letters, as our key. Then we
encipher the message using this key, assuming that we could convey the key somehow to the
intended recipient in a secured channel. Even if Mr. X knows the whole of the ciphertext,
using whatever attack, it is not possible to break this system. Intuitively it is clear that the
longer key gives more safety. This is what Shannon called
Perfect Secrecy.
Question:
Comment on these remarks.
(You may also have a look at [64].)
Remark 3.1
One important thing that we learn from the one-time pad is the value
of randomness for cryptography. Perfect secrecy is possible because the ciphertext
not only looks random to an adversary but is, in fact, random, since Xor-ing non-
random plaintexts with random keys produces ciphertexts as random as the keys,
i.e., uniformly distributed. The system is not practical because it requires keys as
long as the plaintext but in the next section we show how to relax this requirement in
such a way that we can build a scheme that uses short random keys and yet is secure
against real-world adversaries, whose computational power is always limited. This
will be achieved with the use of pseudo-randomness, a weak form of randomness
that makes mathematical objects look random to a computationally bounded adver-
sary (see Definition 3.4 below). We will see that this concept plays a crucial role
in cryptography because one of the main principles guiding the design of encryp-
tion schemes is that the encryption functions should behave like pseudo-random
functions.
