BLOCK CIPHERS, LOGORITHMS, HEXADECIMAL SYSTEM, MISC. 


Block ciphers encrypt blocks of plaintext; the cryptographer
decides on the size of the blocks being used. For instance, if we
wanted to encrypt the ASCII equivalents for the letters a, b, and
c, we would get
                
          (a)        (b)        (c)

        00100001   01100010   01100011


Using a block size of 6, this becomes

                001000/010110/001001/100011

 
LOGORITHMS

Logorithms, in computer science, are a way of taking a given
value and figuring out how much space is needed to represent it
in binary form.

For instance, log10(783) is roughly equivalent to 3
(three digits would be needed to represent this number in binary
form).

A more general rule is that 
                
log2(x) is roughly equivalent to the number of bits
needed to write x in binary


Also, logx(1) will always be ZERO for any x not equal
to 0. (That is because x0 = 1 for any x.)

Good things to know: 

  log2(1000) is roughly equal to 10

  log2(1000000) is roughly equal to 20
                
  y = log2(x) is the same as saying 2y = x

2x is the number of different ways one can fill x bits
(there are x positions that need to be filled, and 2x
possible combinations which could fill them)

Permutations and substitutions

  a substitution requires k*(2k) bits to represent
  a permutation(transposition) requires k*(log2k) power bits


Base-16, or hexadecimal

Base 10 numbers                 Hexadecimal equivalents
0                                       0
1                                       1                                       
2                                       2
3                                       3
4                                       4
5                                       5                       
6                                       6                       
7                                       7                       
8                                       8
9                                       9       
10                                      A
11                                      B
12                                      C       
13                                      D
14                                      E
15                                      F


Examples: 
  2A(base 16) = 42 (base 10)
  10(base 16) = 16 (base 10)
  11(base 16) = 17 (base 10)

If we want to convert "a" in ASCII into hexadecimal form, we take
its binary equivalent first:

  "a" is  01100001

        --and then break that into 4-bit blocks--

                                0110/0001
        --and then determine its value from those blocks--

                                0110= 6
                                0001= 1

        --which leaves us with 61 in base-16, or hexadecimal form.
        

Miscellany:

Moore's Law--Not really a law at all, just an observation that
the speed of CPUs doubles every 1.5 years. It has held pretty
well for thirty years or more years. It cannot hold indefinitely
- there are physical limits - but experts disagree as to how many
more years it will hold.

Parity--In computer science, this refers to whether or not there
is an even number of bits that are ones in a given line of binary
numbers.