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Songs of the Universe
The standard encryption key in Internet security today is 128 bit
SSL. Here we demonstrate how each 'bit' of a key doubles the complexity,
thus making it take twice as long to crack the key with each bit
we add.
Internet privacy and computer security depend entirely on complex
passwords and mathematical algorithms. Here we describe how this
complexity is built So far, no one has managed to break a 128 bit
key - so far. But as computers get faster and cheaper, this may
not always be the case.
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Private Key Encryption |
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Part 1 - Cryptography School
Part 2 - Keys Public and Private
Part 3 - On Complexity and Cracking
Part 4 - Encrypting or Enciphering
Cryptography Part III
On Complexity and Cracking
Encryption relies on encrypting an email message or file in such
a way that it is not easy to decipher without special knowledge,
specifically the password. This requires complexity and complexity
requires time, even for a computer. What it really comes down to
is that for someone without your secret key to break your code,
they would have to try every possible combination of letters and/or
numbers that make up your key.
If we want to be really picky, we don't actually have to try all
possible combinations. On average, we only have to try 50% of them.
That is, on average. However remember averages: If you put one foot
in boiling water, and one foot in ice water, on average you are
comfortable.
Trying all the combinations is called an 'Exhaustive Search', or
a 'Brute Force Attack'. Simple, but given enough time, always
effective. So our goal is to deny the bad guys enough time.
Which brings us back to complexity. Remember the 'bit'? We made
the statement that each bit doubles the complexity of a key. We
need to return to our coin example now in order to show just how
complex these things can get. But we will try to make it fun and
painless (Yeah right, that's what the dentist said).
OK, get out the coins again. Also get some fingernail polish or
paint and paint a '1' on one side of the coins and a '0' on the
other. Since each coin has two sides, we now have a binary number,
which is shown in column 3 below. We painted a '0' on the heads
side to help match our previous example using only two coins.
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Number |
Coins |
Binary # |
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1 |
Heads, Heads |
0 0 |
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2 |
Heads, Tails |
0 1 |
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3 |
Tails, Heads |
1 0 |
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4 |
Tails, Tails |
1 1 |
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We have added the third column so that you can see what the computer
uses for the same states as the coins. We won't keep this up because
the numbers get too long and all the 1's and 0's just look confusing.
We just want you to know that this is what the computer sees.
Now we will show what happens as you add each new coin - uh, bit.
We also show how many combinations can be made with this number of
bits.
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Coins/Bits |
Maximum Combinations |
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1 |
2 |
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2 |
4 |
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3 |
8 |
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4 |
16 |
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5 |
32 |
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6 |
64 |
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7 |
128 |
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8 |
256 |
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9 |
512 |
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10 |
1,024 |
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11 |
2,048 |
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12 |
4,096 |
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13 |
8,192 |
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14 |
16,384 |
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15 |
32,768 |
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16 |
65,536 |
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As you can see, as you add one new coin the numbers double. Yet 16
coins has the same number of bits as only 2 letters of the alphabet.
This is the same thing as saying it is a two-byte number. If you had
to guess which of the 65,536 numbers was the correct one, you would
be guessing for a long time.
But a computer could guess it in just a blink. It is like trying to
lock your computer with a two-letter password. Obviously, we need
more complexity. Let's add some more bits:
| |
Coins/Bits |
Maximum Number |
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17 |
131,072 |
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18 |
262,144 |
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19 |
524,288 |
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20 |
1,048,576 |
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21 |
2,097,152 |
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22 |
4,194,304 |
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23 |
8,388,608 |
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24 |
16,777,216 |
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25 |
33,554,432 |
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26 |
67,108,864 |
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27 |
134,217,728 |
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28 |
268,435,456 |
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29 |
536,870,912 |
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30 |
1,073,741,824 |
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31 |
2,147,483,648 |
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32 |
4,294,967,279 |
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Sorry about the long list, but we went to 32 bits for a reason. 32
bits is only like using a four-letter password. So if you use four-letter
words for your password, the bad guys (assuming your are not they)
must guess over 4 BILLION combinations. That's a lot, right? Wrong.
A computer will guess your four letter word before you can get it
out of your mouth. If we want Internet privacy and computer security,
we will certainly need better passwords than this.
We won't carry on with more examples. We're sure you get the point:
We need more complexity. We have shown you numbers only 10 digits
in length, and done so with only four characters.
By the time you get up to even 56 bits - a simple 7 character password
used by the Government's Data Encryption Standard (DES), the possible
combinations are astronomical: 72,057,594,037,927,936 possible combinations
to be precise. We will let you figure out how many combinations there
are in the Internet's 128 bit SSL keys.
Using a very fast PC available on today's market, it would take tens
of thousands of years to break even this simple 7 character password,
so we ought to feel pretty safe. No longer true, however. We will
show you why in the next exciting section. We know you can't wait,
so we won't take a break here. Let's get on with
Encrypting or Enciphering (same thing)
Back to top...
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Songs
of the Universe goes on-line. The first encryption
program to combine the power of One-Time Pads with the speed
of streaming ciphers and totally random keys to produce one
of the strongest encryption systems ever!
You can download a FREE copy of the SOTU
decryptor here! |
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Do you have a humorous story, preferrably
true that others might enjoy?
Send it to us!
Meanwhile, here is our favorite from darwin awards
A man in Texas was killed while chasing a half full can of beer
when it rolled out onto the highway.
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