Brian Foster wrote:
> |[ ... ]
> | (Pi and e you can always calculate (predict) more digits. They are
> | irrational, not random).
>> careful here. if I told you I'm using the base 10
> expansion of π and my current “random” digit is 7,
> you wouldn't be able to tell me what the next digit
> is. (you'd be able to guess with an c.10% chance
> of being right.) and if I asked you for the next
> sequence of, say, 10 digits, your search space is
> larger. what we don't know is just how large.
>>If you told me your last ten* "random" digits though, you might be in
You can't know anything from a single input. My suggestion was that with
suitable amount of history, that if you have calculated the irrational
number to more places than was used, you could deduce which irrational
number was used and thus what part of it might be used next. Hypothetically.
I suppose if you somehow had a method to generate a long sequence of
digits far past the number of places currently calculated or could be
calculated by anyone in a reasonable time then such an irrational
number could be useful. I'm not expert enough on irrational numbers or
cryptography. I'm not even in the same planet as Hibert, Knuth, Hoare,
Schieer & etc.
*Or whatever needed depending on what ever algorithm you are using,
which of course if it was Open Software would be known.
The point is that with any reasonable publicly used cryptology most
of the bits of the PRNG are known. All public / private key and
all non-OTP systems are a compromise. The only 100% secure for
ever system is a One Time Pad using a true random key the same
size at least as the message. If there is no method somewhere of
true randomness in the compromise non-OTP systems then the keyspace is
smaller (easier to brute force) than the size of key suggests.
Weather reports sent in code was the downfall of one encryption system.
(The British sent a Trawler to monitor the same weather). If you know
enough of plain text then you can work out what the key is. The 2nd
worse case is key the same size as message, then you need all the plain
text to get the key. The worst case is OTP with key same size as
message, because then recovering the key is worthless as the next
message uses a new one. The Germans in WWII used two quite good systems
and compromised both for different reasons. The Japanese systems in WWII
were mostly all broken due to research & educated guesses at the plain
text. All of these systems would be quite robust against modern brute
force computer attack. The problem was how the systems where used.
Japanese Codes: The Emperor's Codes by Michael Smith
Enigma was *one* German system. Most of the compromise was because the
British knew the algorthim (A captured machine) and mistakes by German
operators. The other was the Lorentz Machine, Colossus
<http://en.wikipedia.org/wiki/Colossus_computer> was used to decode
Lorentz Traffic. The algorithm was compromised by the same message sent
twice on same settings allowing the key and thence machine structure to
be deduced. Weather reports sent by Lorentz in conjunction with the
British knowing the Weather via observation near the same place, allowed
Colossus operators to quickly get the new key each day. By hand it would
have taken six weeks. http://www.codesandciphers.org.uk/lorenz/fish.htm
A study of codebreaking over the last 80 years reveals that the biggest
problem is arrogance by the users.
Messages to spies from 1950s to now probably uses OTP. Famous of these
may be the Short Wave Number Stations. I first heard them in the 1970s
and they are still on the go
Interesting R4 program on it and may have download here
AFAIK no number station content has ever been broken.
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