Re: A89: Linux Port for 89/92


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Re: A89: Linux Port for 89/92




Based on what the FAQ says:

RSA works as follows: take two large primes, p and q, and compute their
product n = pq; n is called the modulus. Choose a number, e, less than n and
relatively prime to (p-1)(q-1), which means e and (p-1)(q-1) have no common
factors except 1. Find another number d such that (ed - 1) is divisible by
(p-1)(q-1). The values e and d are called the public and private exponents,
respectively. The public key is the pair (n, e); the private key is (n, d).
The factors p and q may be kept with the private key, or destroyed.

I gather that p and q are primes, and the only two factors (excluding 1) of
n are p and q.  But, I don't think I understand what n equals...  n cannot
equal 512, first of all, because it is an even #, so I reread what you wrote
and read 'We have "n" (=a large 512-bit number)' so is 1<n<2^512??  Does
this mean that we are dealing with a number that could be as large as
13,407,807,929,942,597,099,574,024,998,205,846,127,479,365,820,592,393,377,7
23,561,443,721,764,030,073,546,976,801,874,298,166,903,427,690,031,858,186,4
86,050,853,753,882,811,946,569,946,433,649,006,084,096
?? (actually, a little less than that, because that # doesn't have only 2
factors... hehe, it has 512 of them!! =)

What I suggest is that someone with a really fast computer make a program to
start at 2^512-1 and find the factors of that #, and if there are only 2, to
put them in a list, then decrease the # by 2 and do it again.  I'm not
saying that it'll give the answer right away, since there are trillions and
trillions of digits in each number, but then we will have a list of all of
the _possible_ values of n, p, and q.

-Miles Raymond      EML: m_rayman@bigfoot.com
ICQ: 13217756       IRC: Killer2        AIM: KilIer2 (kilier2)
http://www.bigfoot.com/~m_rayman/

----- Original Message -----
From: Johan <johei804@student.liu.se>
To: <assembly-89@lists.ticalc.org>
Sent: Wednesday, July 14, 1999 12:05 PM
Subject: Re: A89: Linux Port for 89/92


> The ROM is mostly written in C, but barely optimized. Some parts, like
> hardware initialization and low-level math routines, are written in asm.
>
> The .tib file contains "chunks" of information, the largest chunk is the
> code-chunk. Other chunks contains the name of the OS, the version, and
other
> more or less important things. The very last chunk contains an 512-bit RSA
> crypto that, when decrypted, is an MD5 checksum of all other chunks.
>
> This checksum is compared to the checksum that the boot loader calculates
> when it installs the .tib file.
>
> There is no encrypted or otherwise hidden code anywhere. There are
functions
> in the ROM for both encryption and decryption, if you can supply the
*key*.
> The key needed for decryption is in the ROM (of course, since the boot
> loader uses it), I've found it. But the key needed for *encryption* is not
> available, only TI knows about it.
>
> Please see the RSA Labs FAQ for more information about the RSA encryption
> scheme (question 3.1.1): http://www.rsa.com/rsalabs/faq/
> We have "n" (=a large 512-bit number) and "d" (=17) in the example.
> This FAQ also discusses many ways to "break" RSA.
>
> file://Johan
>
> KKokiri89@aol.com wrote:
> >
> > Is there any way to decompile or take apart the TIB rom file? Does
anyone
> > know what language it is written in? I thought it was C, but of course i
have
> > learned many new things in this past week. The encryption is incredible,
but
> > i guess it's not too surprising. You said we have the decrypted
password, but
> > i didn't see it in the letter. Could you tell what it is and then,
(maybe) we
> > can begin to understand this. That is a serious problem that will have
to be
> > addressed. There is no way that we could break the code by chance,
but...what
> > if we could look at what the encrypted code was in the boot loader? Or
is the
> > boot loader like firmware and can't be decompile or taken from the
> > calculator.
> > Some thing we could try is connecting a calculator to the
computer...fire up
> > the VTI, then send a ROM file to the VTI, pause it and look at the boot
> > loader code...of course that would still be very complicated.
> >
> > (Imagine what TI is going to do if we do get past the encryption! They
will
> > probably make it so that we can't load the next released ROM, or find
some
> > way to punish us....hehe)
> > (if we ever do get past it.....yeah right!)
> >
> >
> > Kyle



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