vernonner3voltazim

2004-10-30 04:38:34 UTC

You may be aware that when you take the reciprocal

of a prime number P, its period often has length

P-1. Actually, if you try enough numerical Bases

(Base Two, Base Three, etc), you will ALWAYS fine

a period of P-1 in at least one Base, and often

many. (Meanwhile, composite number C never has

a period of C-1 in any Base.)

So you can take the reciprocal of some number on

the order of one hundred million, and Base Two,

and quickly and easily end up with a hundred

million pseudorandom digits. In fact, because

it is so easy, you can take reciprocals (or other

divisions) near-simultaneously with a whole bunch

of primes, and combine their results to get a

pseudorandom sequence which can approach the

perfectly random condition arbitrarily closely.

Then you use those digits for "one-time-pad"

encryption. I've written a program to try this

method, specifically to encrypt files. In theory

the program's encryption level starts at about

64,000 bits, and goes up from there. You can

find/study it at:

https://sourceforge.net/project/showfiles.php?group_id=122468&package_id=134066&

release_id=278616

I hope I haven't introduced any weaknesses in

implementing it. Let me know! Thanks!

of a prime number P, its period often has length

P-1. Actually, if you try enough numerical Bases

(Base Two, Base Three, etc), you will ALWAYS fine

a period of P-1 in at least one Base, and often

many. (Meanwhile, composite number C never has

a period of C-1 in any Base.)

So you can take the reciprocal of some number on

the order of one hundred million, and Base Two,

and quickly and easily end up with a hundred

million pseudorandom digits. In fact, because

it is so easy, you can take reciprocals (or other

divisions) near-simultaneously with a whole bunch

of primes, and combine their results to get a

pseudorandom sequence which can approach the

perfectly random condition arbitrarily closely.

Then you use those digits for "one-time-pad"

encryption. I've written a program to try this

method, specifically to encrypt files. In theory

the program's encryption level starts at about

64,000 bits, and goes up from there. You can

find/study it at:

https://sourceforge.net/project/showfiles.php?group_id=122468&package_id=134066&

release_id=278616

I hope I haven't introduced any weaknesses in

implementing it. Let me know! Thanks!