Cryptography Reference
In-Depth Information
The other four AES finalists can also be shoehorned into this
model of alternating rounds of confusion and diffusion. All of them
are considered to be quite secure which means they all provide more
randomization.
2.2.2 Public-Key Encryption
Public-key encryption systems are quite different from the popular
private-key encryption systems like DES. They rely on a substantially
different branch of mathematics that still generates nice, random
white noise. Even though these foundations are different, the results
are still the same.
The most popular public-key encryption system is the RSA algo-
rithm that was developed by Ron Rivest, Adi Shamir, and Len Adle-
man when they were at MIT during the late 1970s.Ron Rivest, Adi
Shamir, and Len Adleman The system uses two keys. If one key en-
crypts the data, then only the other key can decrypt it. After the en-
cryption, first key becomes worthless It can't decrypt the data. This
is not a bug, but a feature. Each person can create a pair of keys
and publicize one of the pair, perhaps by listing it in some electronic
phone book. The other key is kept secret. If someone wants to send
a message to you, they look up your public key and use it to encrypt
themessage to you. Only the other key can decrypt this message now
and only you have a copy of it.
In a very abstract sense, the RSA algorithmworks by arranging the
set of all possible messages in a long, long loop in an abstract math-
ematical space. The circumference of this loop, call it
,iskepta
secret. You might think of this as a long necklace of pearls or beads.
Each bead represents a possible message. There are billions of bil-
lions of billions of them in the loop. You send a message by giving
someone a pointer to a bead.
The public key is just a relatively large number, call it
n
. Amessage
is encrypted by finding its position in the loop and stepping around
the loop
k
steps. The encrypted message is the number at this posi-
tion. The secret key is the circumference of the loop minus
k
.Ames-
sage is decrypted by starting at the number marking the encrypted
message and marching along the
k
steps. Because the numbers
are arranged in a loop, this will bring you back to where everything
began- the original message.
Two properties about this string of pearls or beads make it possi-
ble to use it for encryption. The first is that given a bead, it is hard
to know its exact position on the string. If there is some special first
bead that serves as the reference location like on a rosary, then you
n − k
