A non-working prototype of a compression scheme.
Alice, and Bob share a large list of prime numbers, indexed by their occurence in The Sequence of Prime Numbers.
For illustration purposes:
0 | 2 1 | 3 2 | 5 3 | 7 4 | 11 . . .
Alice, after encrypting data in an ideal cryptographic scheme, would like to further compress this message. *which would result in a uniformly-distributed sequence of zeros and ones
Alice proceeds with the following sequence of actions:
-- Blocking
- Alice breaks the message, M, into a sequence of submessages, {M_i} each consisting of N bits,
- N is an integer for which it is always tractable for Alice to quickly "distill"
- Quickly meaning, faster than the period of the PPS of the channel
-- Distilling For each submessage, M_i
- Alice "distills" the message by:
- factor M_i into its prime factors, or
- identify that it, M, itself is prime
- Record the result into {P_j, j, n} Where:
- P_j is the prime factor
- j is the index, in the sequence of all primes
- n is the number of repetitions of P_j
- This process takes at most sqrt(N) by the Fundamental Theorem of Arithmetic
-- Encoding
- For each submessage, M_i Alice encodes as follows:
- Produce a message D, comprised of
- j in binary
- n in binary
- Within D, identify the shortest "non-occurent" sequence s
- Modify D to escape after each j and each n with the sequence s
- Prepend D with an escaped header identifying s
- Produce a message D, comprised of
Alice transmits D to Bob