hacking-the-art-of-exploitation

and diffusion. Confusion refers to methods used to hide relationships between
the plaintext, the ciphertext, and the key. This means that the output bits
must involve some complex transformation of the key and plaintext. Diffusion
serves to spread the influence of the plaintext bits and the key bits over as
much of the ciphertext as possible. Product ciphers combine both of these
concepts by using various simple operations repeatedly. Both DES and AES
are product ciphers.
DES also uses a Feistel network. It is used in many block ciphers to
ensure that the algorithm is invertible. Basically, each block is divided into
two halves, left (L) and right (R). Then, in one round of operation, the new
left half (L i ) is set to be equal to the old right half (R i−1 ), and the new right
half (R i ) is made up of the old left half (L i−1 ) XORed with the output of a
function using the old right half (R i−1 ) and the subkey for that round (K i ).
Usually, each round of operation has a separate subkey, which is calculated
earlier.
The values for L i and R i are as follows (the ⊕ symbol denotes the XOR
operation):
L i
= R i−1
R i = L i−1 ⊕ f(R i−1 , K i )
DES uses 16 rounds of operation. This number was specifically chosen to
defend against differential cryptanalysis. DES’s only real known weakness is
its key size. Since the key is only 56 bits, the entire keyspace can be checked
in an exhaustive brute-force attack in a few weeks on specialized hardware.
Triple-DES fixes this problem by using two DES keys concatenated
together for a total key size of 112 bits. Encryption is done by encrypting the
plaintext block with the first key, then decrypting with the second key, and
then encrypting again with the first key. Decryption is done analogously, but
with the encryption and decryption operations switched. The added key size
makes a brute-force effort exponentially more difficult.
Most industry-standard block ciphers are resistant to all known forms of
cryptanalysis, and the key sizes are usually too big to attempt an exhaustive
brute-force attack. However, quantum computation provides some interesting
possibilities, which are generally overhyped.
0x731
Lov Grover’s Quantum Search Algorithm
Quantum computation gives the promise of massive parallelism. A quantum
computer can store many different states in a superposition (which can be
thought of as an array) and perform calculations on all of them at once.
This is ideal for brute forcing anything, including block ciphers. The superposition
can be loaded up with every possible key, and then the encryption
operation can be performed on all the keys at the same time. The tricky part
is getting the right value out of the superposition. Quantum computers are
weird in that when the superposition is looked at, the whole thing decoheres
into a single state. Unfortunately, this decoherence is initially random, and
the odds of decohering into each state in the superposition are equal.
Cryptology 399