One-time pad: take a different random number for every character in the plaintext
Attack acronyms, for reference:
TODO find more examples for indistinguishability and malleability
The one-time pad is malleable
TODO research malleability more
One interesting topic is: fully homomorphic encryption.
Apparently this type of encryption is possible but still too slow to be practical.
A related topic is to make ciphertexts searchable without decrypting them. Unclear how feasible this is.
Entropy is the measure of uncertainty or disorder in a system.
The entropy is
p_1 * log(p_1) - p_2 * log(p_2) - ... p_n * log(p_n)
p in the above is the probability for each bit -- your "probability distribution".
In a binary string with uniform probability distribution (ie. each bit has equal probability), then each
p is equal to
2^-128 where 128 is the lengthe of the string.
With this uniform probability, the entropy will always have
128, or whatever the length of the bits is.
An entropy equal to the lenth of the string says the distribution is uniform.
When a system does not have uniform probability (ie a coin where heads is
1/10 and tails is
9/10) then you will have an entropy less than the length of the string (ie. 0.469).
These take input from the analog outside world to generate random data -- acoustic noise, static electricity, air turbulence, temperature, operating system I/O, etc.
Real randomness can come from quantum sources: photon polarization, vacuum fluctuations, radioactive decay. This is bizzarre. If randomness just means a high amount of unpredictability, that implies all systems are nevertheless potentially predictable, given enough time, data, and models -- then how could real randomness ever exist?
These take short random bits from RNGs and use them to expand a longer stream.
There are non-cryptographic PRNGs which are mainly used for simulations and video games; their main concern is the quality of the bits' probability distribution but may be predictable, so are not good for cryptography.
something like pi is a good PRNG because it has no patterns -- new digits are unpredictable. However it is not a RNG because it is deterministic.
TODO implement mersenne twister in JS^ Up