Re: Internet Privacy Guaranteed ad (POTP Jr.)

At 10:08 PM 2/20/96, IPG Sales wrote:

>Unlike Mr. Silvernail, we have a much simplier definition of what we mean
>by a one time pad - given a message/file of length N, where N is a finite
>practical number say less than 10 to the 1000th power, that the encrypted
>ciphertext can be any of the N to the 256th power possibile clear/plain
>text messages/files.  To prove that the IPG system does not work, all you
>have to do is to prove that is not the case - that our system, without
>artifically imposed boundary conditions will generate a subset of those
>possibilities  - that is simple and strsight forward - not
>hyperbole but action - everyone stated how simple it was to break the system,
>now everyone is back paddling aa fast as they can, like Mr. Metzger and
>some of the other big bad cyphermouths.

PROOF:

        Given that N is the length of the message in bits. The number of
possible combinations of bits is 2^N.  For any message length N > 1,
2^N < N^256.  Simple example.  Message length is 3 bits.  The maximum
number of possible combinations of these bits is 8.  This is far less than
3^256 (which is more than 10^100, i.e. it overflows the calculator on my
Mac).  Sorry guys.  Try learning some simple math before you try and sell
crypto.

        Clay

---------------------------------------------------------------------------
Clay Olbon II            | olbon@dynetics.com
Systems Engineer         | ph: (810) 589-9930 fax 9934
Dynetics, Inc., Ste 302  | http://www.msen.com/~olbon/olbon.html
550 Stephenson Hwy       | PGP262 public key: finger olbon@mgr.dynetics.com
Troy, MI 48083-1109      | pgp print: B97397AD50233C77523FD058BD1BB7C0
    "To escape the evil curse, you must quote a bible verse; thou
     shalt not ... Doooh" - Homer (Simpson, not the other one)
---------------------------------------------------------------------------

Yes, in trying to answer all the questions you that were posed, we made 
that mistake, obviously it was a typo - unlike so many of you, we are not 
perfect - the 10 to the 1000 is correct though

On Wed, 21 Feb 1996, Clay Olbon II wrote:

> At 10:08 PM 2/20/96, IPG Sales wrote:
> 
> >Unlike Mr. Silvernail, we have a much simplier definition of what we mean
> >by a one time pad - given a message/file of length N, where N is a finite
> >practical number say less than 10 to the 1000th power, that the encrypted
> >ciphertext can be any of the N to the 256th power possibile clear/plain
> >text messages/files.  To prove that the IPG system does not work, all you
> >have to do is to prove that is not the case - that our system, without
> >artifically imposed boundary conditions will generate a subset of those
> >possibilities  - that is simple and strsight forward - not
> >hyperbole but action - everyone stated how simple it was to break the system,
> >now everyone is back paddling aa fast as they can, like Mr. Metzger and
> >some of the other big bad cyphermouths.
> 
> PROOF:
> 
>         Given that N is the length of the message in bits. The number of
> possible combinations of bits is 2^N.  For any message length N > 1,
> 2^N < N^256.  Simple example.  Message length is 3 bits.  The maximum
> number of possible combinations of these bits is 8.  This is far less than
> 3^256 (which is more than 10^100, i.e. it overflows the calculator on my
> Mac).  Sorry guys.  Try learning some simple math before you try and sell
> crypto.
> 
>         Clay
> 
> ---------------------------------------------------------------------------
> Clay Olbon II            | olbon@dynetics.com
> Systems Engineer         | ph: (810) 589-9930 fax 9934
> Dynetics, Inc., Ste 302  | http://www.msen.com/~olbon/olbon.html
> 550 Stephenson Hwy       | PGP262 public key: finger olbon@mgr.dynetics.com
> Troy, MI 48083-1109      | pgp print: B97397AD50233C77523FD058BD1BB7C0
>     "To escape the evil curse, you must quote a bible verse; thou
>      shalt not ... Doooh" - Homer (Simpson, not the other one)
> ---------------------------------------------------------------------------
> 
> 
>

Clay writes:
>         Given that N is the length of the message in bits. The number of
> possible combinations of bits is 2^N.  For any message length N > 1,
> 2^N < N^256.  

Uh, nope. 2^N grows asymptotically faster than N^256. Actually, for any 
constants A and B, A^N grows asymptotically faster than N^B. For A=2, B=256,
the crossover happens somewhere before N=4096. 
2^4096 = 2^(16*256) > 2^(12*256) = (2^12)^256 = (4096)^256

If the IPG people are using N=5600 (weird choice) then certainly 
2^5600 > 5600^256, for what little that's worth.

(Ah, my computer science B.S. pays off ;)

-Lewis	"You're always disappointed, nothing seems to keep you high -- drive 
	your bargains, push your papers, win your medals, fuck your strangers;
	don't it leave you on the empty side ?"  (Joni Mitchell, 1972)

> > [ IPG Sales ]
> >
> >... any of the N to the 256th power possibile clear/plain text
> >messages/files.

Excuse me?  256^N.

> [ Clay Olbon ]
> PROOF:
> 
> For any message length N > 1, 2^N < N^256.

Excuse me?  2^N is not O(N^k).

Cypherpunks used to be a place where I could fairly reliably see
high-SNR commentary from real cryptographers/number theorists.
Now we have the blind replying to the blind's obfuscatory
nonsense, and the useful posts take some effort to find.

> Try learning some simple math before you try and sell crypto.

Surely it's not a requirement these days.

Peter Monta   pmonta@qualcomm.com
Qualcomm, Inc./Globalstar