- #1
sysprog
- 2,617
- 1,796
How do we distinguish the decimal expansions of irrational numbers, and products thereof, from random sequences?
Is
an arbitrarily specified (not claimed to be perfectly randomly selected) numeric string,
e.g.
the 10^10th to 10^19th digits of the decimal extraction of the square root of 2.2, IFFd against (modulo 2 binarily subtracted from) or XORd against (modulo 2 binarily added to) a same-length sequence of some other cut from some similarly generated decimal expansion,
just as random-appearing
as is,
e.g.
an XOR of a digitization of 2 microwave background radiation streams taken from 2 different radio telescope arrays
?
The expansion products can be algorithmically specified briefly, while the observation products cannot be definitively expressed in brief.
If I don't tell anyone how I generated a long number sequence, and it isn't psuedorandom in the sense of using a short random seed to generate a long PRN that after a long period repeats, unless my generation routine has some predictability, how could it be discerned given only its output?
Might that idea have an applicability to strong cryptography with manageably short keys?
Could I transmit a brief specification of an arbitrarily long irrational number product decimal expansion sequence, and thereby produce a key for a symmetric encryption/decryption surjective function, that was hard-to-guess based on how hard to guess my generation method was, or might my pattern render the generation procedure specification, based on its short length, more easy to infer than the generated sequence would be to guess?
Is
an arbitrarily specified (not claimed to be perfectly randomly selected) numeric string,
e.g.
the 10^10th to 10^19th digits of the decimal extraction of the square root of 2.2, IFFd against (modulo 2 binarily subtracted from) or XORd against (modulo 2 binarily added to) a same-length sequence of some other cut from some similarly generated decimal expansion,
just as random-appearing
as is,
e.g.
an XOR of a digitization of 2 microwave background radiation streams taken from 2 different radio telescope arrays
?
The expansion products can be algorithmically specified briefly, while the observation products cannot be definitively expressed in brief.
If I don't tell anyone how I generated a long number sequence, and it isn't psuedorandom in the sense of using a short random seed to generate a long PRN that after a long period repeats, unless my generation routine has some predictability, how could it be discerned given only its output?
Might that idea have an applicability to strong cryptography with manageably short keys?
Could I transmit a brief specification of an arbitrarily long irrational number product decimal expansion sequence, and thereby produce a key for a symmetric encryption/decryption surjective function, that was hard-to-guess based on how hard to guess my generation method was, or might my pattern render the generation procedure specification, based on its short length, more easy to infer than the generated sequence would be to guess?
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