Ticker Applet
Elementary Data Encryption:
Data Scrambling For Privacy.



State- of- the- art cryptography is not really the subject of much open discussion, but much more basic techniques will suffice as far as casual snoopers of the general public are concerned: There is virtually no limit to the possibilities provided for data encryption by digital processing. Here is a simple encoder process:

Fig.12: Scrambled Text Image Example

Encoder Example
Fig.13 Encoder Process

Encoder Process



The microprocessors' primitive operations, such as addition, subtraction, exclusive or, and left/ right rotation by a variable number of places first come to mind. It is fair to say that anybody trying to crack the code will also try these options first! If it is required for the output values to occupy the same range as the input data, some modifications are needed: Sums must be taken modulo the highest number in the data plus one; The highest number in the data must be added to any differences which are negative; For rotation, any bits falling off the MSB must be fed back via the LSB and vice versa. Two operands are required by those operations, so what is the second operand? It can be a delayed or shuffled copy of the same data, a password, or even a completely different text (which must somehow be made known to the recipient.)

Implementing a random mapping (a substitution operation by using a look- up table) looks superficially attractive, but some care is necessary: Cascading two or more random mapping stages will provide no encryption advantage, unless there are intervening stages employing scrambling which uses two or more operands. This way, it is impossible to find a single random mapping stage which is equivalent to the overall effect of several cascaded random mapping stages.

Using a transform (or matrix multiplication) provides superior encryption performance, as long as the inverse matrix exists, so that the original file can be retrieved. Again, cascading two or more transform stages does not improve the cipher security, unless they are interspersed with stages employing operations like exclusive or and left/ right feedback rotation. This ensures it is impossible to find a single matrix that provides the same effect as the combination of several cascaded matrix stages! Is is most important to actually implement the number of stages intended. If it is required for the input and output data to share the same range of values, the Number Theoretic Transform (NTT) can be useful.

It is possible to use exactly the same procedure for both encoding and restoring the data, but this does limit options a lot, and only saves a few lines of program data. For an encoder made of alternating random mapping and matrix stages, the total number of permutations (and output combinations) is a product of n main terms:

Pi=1..nm.v!

Where



For each stage using a transform (vli)! is substituted for m.v! The value of 'm' depends on the relative block lengths of consecutive stages. There is no need for the block length, rearranging, and scrambling rules to be the same for all stages. For certain values of n, li and v, the number of different possible encoder outputs is beyond the realm of personal computing. As any private individuals wishing to eavesdrop on the data do not know any of these parameters, theirs is no average task! (It is not suggested that such a level of security has been incorporated in figure 12, which is merely meant for illustration: The lower half is encoded into the top half.)

You have probably noticed there is also a new animated fractals section.


Electronics links:
  • Simplified Analog Electronics Simulation
  • Data converters
  • Video Digitizer
  • Thermionic valves look like depletion nMOS
  • Transient response
  • Under 50- chip discrete Microcontroller
  • 2x OverSampling Digital Filter Click Here!
  • More Simulation: Finite Elements For electrostatic Field Computation

    Computing Projects:
  • Computer Chess
  • Fractal Automata! Click here!
  • Discrete Correlation
  • RLE For Image Compression
  • Discrete Convolution For Image Processing
  • Newton's Method For Complex Polynomials
  • Computer Games: Mastermind

  • Non- frames version

    The distinction is somewhat arbitrary: Most of the electronics sections involve use of a computer to some extent, and vice versa.

    1