2**64=18446744073709551616
2**32=4294967296
does this clarify what Jeff is trying to explain to you 2**64 IS a VERY much
larger number of possible combinations if you are allowing for all numbers
up to 2**64. Encrypting the 64 bit number to a 32 bit number would amount to
something along the lines of probabilistic encryption where any resulting
cyphertext (encrypted number) could have been created by a number of
different keys given the same plaintext (non encrypted number), in this case
something resembling 2**32 different keys!(if I have this figure wrong
please somebody correct me). The exception to this would be if you are
creating a 32 bit HASH of the 64 bit number but I know of no algorithm that
does this, there are others that use larger numbers such as SHA-1 and MD5
but these work with larger numbers. Given the above calc's it looks like you
are going to get a LOT more than just repeats of it twice you will get them
(2**32)+1 times or am I wrong here......(VERY LATE NIGHT + VERY EARLY
morning = questionable maths) ;-)

P.S I recommend that you read Applied Cryptography by Bruce Schneier

Regards Jonathan

-----Original Message-----
From: pic microcontroller discussion list
[mailto:PICLIST@MITVMA.MIT.EDU]On Behalf Of Jan-Erik Soderholm
Sent: Tuesday, 22 October 2002 11:08 PM
To: PICLIST@MITVMA.MIT.EDU
Subject: Re: [PIC]: Exporting data from MPLAB SIM to MSoft Excel or Text


  # possible 64 bit numbers         2**64
  --------------------------   =  --------   =  2**(64-32)   =  2**32
  # possible 32 bit numbers         2**32

(2**64 - 2**32) *is* a much larger number, but it's not the number
we are talking about here, I belive. Try it with smaller numbers
like :

  2**8     256
  ---- =   ---     =  8  =   2**3    =   2**(8-5)
  2**5      32


Jan-Erik Svdrholm.


>> A 64 bit number can hold 2**64 different values.
>> A 32 bit number can hold 2**32 different values.
>>
>> Thus, if your 64 bit number can have *any* value, your
>> 32 bit ("encrypted") numbers vill each have 2**(64-32),
>> or 2**32 duplicates. At least. Best case.
>> That's a bit more then "twice"...
>>

> I believe that should be 2**64 -2**32 duplicates
> a much larger number
> Jeff

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