encryption is a method of taking some data anyone can understand
we call it PlainText and transforming it into something
no one can understand a CipherText, we wish only the person who
encrypted the text(and possibly other people working with him)
to be able to convert the CipherText back in to PlainText,
here we have a problem, In Cryptology it is normally assumed
everyone knows the algorithm used for encryption and decryption.
If everyone knows the algorithm what is to stop anyone from
deciphering the stuff I encrypt.
Here comes in the key, we make the encryption algorithm key dependent
The Encryption allgorithm will take both a PlainText P and a
key K and return ciphertext C. In decryption we take C and K and return
P, or mathematicly:
E(P,k)=C
D(C,K)=P

we would like it to be reletvly easy to compute the two tasks above
yet, we want it to be exreamly difficult(pracecly impossible) to
take C and find P without k, or to take C and P and find k.
No matter what the encryption algorithm is the attacker will always
have the option of attacking with bruteforce, i.e attempt all possible
values of K, and check which one fits.
If K is small in length there are few options for differnt values
of K, and this attack will take a reasonable amount of time.

if K has n bits, there are 2^n possible values for k, and if
it takes time T to check a specific key, It takes on average:
T*2^(n-1) time to break the cipher by brute force.
since we want to keep T small, We must have a large n.

To put some numbers in it, DES was a very common cipher until
just lately, introduced by IBM in 1970(with help from the NSA)
DES has a key of length 55bits, it takes a Pentium III computer 500
clock cycles to compute DES encryption.
a P3 1000Mhz computer can therfor compute 2,000,000 DES encryptions
every second.
It whould still take one such computer many years to hack this
cipher, but 20,000 such computers co-operating over the net can and
did do it. Several years ago someone built a special machine
to Crack DES, which can do the samething in a wapping 2.5 hours.

DES is no longer safe!

AES has a minimum of 128bits in its key, there is today
no known method to attack AES effectivly.