OS upgrade files

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Revision as of 13:37, 3 October 2010 by ExtendeD (talk | contribs) (Fix RSA key links)
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The latest versions of the TI-Nspire and TI-Nspire CAS Operating System are available here. This article describes the format and content of the current versions (v1.1.9253 and v1.1.9170) of the .tno and .tnc files.

.tno/.tnc

A .tno file is an OS image for the TI-NSpire. A .tnc is for the TI-Nspire CAS. Contrary to other calculators with flash memory, the whole OS file is received before being written to flash memory. This is possible thanks to the huge amount of RAM available on the TI-Nspire. Sending a .tno to a TI-Nspire CAS is possible and vice-versa, but at the end of the reception a message will be displayed by the Computer Link Software indicating that the file is corrupted, and the OS won't be installed.

A .tno/.tnc is a PK-Zip file with a custom ASCII header describing the OS update file. It can be opened with a simple archiving program such as WinRAR or WinZip. The PK-Zip file contains a certificate file (TI-Nspire.cer) and a .img file (TI-Nspire.img). OS 1.4, it also contains boot2.cer and boot2.img. Here is an example of .tno/.tnc header (lines starting with # are added comments): 

# File, version, size of the file, ?
 TI-Nspire.tno 1.1.9253  3092555 0
 # __RES__, version, ?, size of the compressed file system once decompressed
 __RES__ 1.1.9253 0  2420072
 \0x1A

The header can have a variable size and is terminated by the byte 0x1A. The sizes in the header are used both to validate on the TI-Nspire side that there is enough available memory to install the new OS (the validation is performed as soon as the header has been received), and at the end of the transfer to ensure that everything has been received as expected. The sizes must be positive integers and must be present, else an error is returned to the Computer Link Software. Multiple spaces are ignored by the parser. The parser seems to read sizes of more than 7 digits incorrectly, accepting some huge sizes, but rejecting other huge sizes and asking for free space of random size.

TI-Nspire.cer

The file follows TI's standard certificate format used on many caculator models. See TIGCC's documentation for more information (more particularly cread and cfindfield).

This file hasn't change between the different upgrades released by TI, up to version 1.7, and is the same for CAS and non-CAS TI-Nspire.

(Format of the following section: Field ID (hex) - size (dec) : comment. The indentation corresponds to subfields.)

350 - 298 : top-level field, similar to TI-68k's FLASH_APP_CERT (0x0300), PRODUCT_CODE (0x0320), FLASH_ROM_CERT (0x0330), etc.

0010 - 4 : ?
0100 - 4 : Revision Number (same field as for the TI-68k)
0260 - 140 : 1024-bit RSA public key used for validating both CAS and non-CAS OSes.
0260 - 140 : 1024-bit RSA public key

240 - 128 : Same field ID as in the .tno/.tnc. Certificate signature, validated using a key hard-coded inside BOOT2 (its modulus is EDBF3336...)
FFF0 - 0 : END_OF_CERT

TI-Nspire.img

Structure

As for TI-Nspire.cer, the file is organized as a certificate.

(Format of the following section: Field ID (hex) - size (dec) - @TI-Nspire: offset of the current version (hex) - @TI-Nspire CAS: offset): comment. The indentation corresponds to subfields.)

8000 : OS

8040 : Product Name: "TI-Nspire"
8010 : First part of Product ID
80E0 : Different on TI-Nspire and TI-Nspire CAS
8020 : OS version
8020 : Minimum OS version after installation. Downgrade to OS versions lower than this one won't be allowed. "1.1.x" for OS <= "2.0.x", "1.7.x" for OS "2.1.x" (i.e. OS 2.1 cannot be downgraded to OS 1.1 for instance).
8080 - 8 : The first 4 bytes are the OS base address: address to which the OS will be copied by boot 2(0x10000000). The 4 next bytes define the format of field 8070 (OS code) : 2 (compressed), 4 (raw), 6 (encrypted and compressed). 6 is currently used.
0320 - 6 : Product code : 0
80F0 - 64 : Blowfish-encrypted version of the previous fields (8040, 8010, 80E0, 8020, 8080, 320)
8210 : ? 24ED68 on TI-Nspire, 0BA9CB on TI-Nspire CAS
8200 : PK-Zipped file system, see further.
8070 - TI-Nspire:2403720, TI-Nspire CAS:2339224 - @TI-Nspire: A7F36, @TI-Nspire CAS: 490E2: Blowfish-encrypted and PK-Zipped OS code. The size is a multiple of 32.

0240 (024D) - 128 - @TI-Nspire: 2F2CBE, @TI-Nspire CAS : 28427A: the signature of the .img, similar to TI-68k's 64 bytes long field 0200. This field is big endian. This signature is validated using the first public key stored in TI-Nspire.cer.
FFF0 - 0 : END_OF_CERT

The crypted field 8070 is 195568 bytes longer in the .tno than in the .tnc, that is the TI-84 Plus emulator of the TI-Nspire would be ~200kb bigger than the CAS of the TI-Nspire CAS! May be the two OS integrates a CAS, but it is not enabled on the TI-Nspire.

Directory Listing

Directory listing of ti-nspire.img (TI-Nspire CAS version), from WinRAR 3.71. 

.\
 \documents\
           \MyLib\
                 \linalgcas.tns             (TI-Nspire Document)
 \phoenix\
         \clnk\
              \locales\
                      \da\
                         \strings.res
                      \de\
                         \strings.res
                      ...
         \ctlg\
              \locales\
                      \da\
                         \strings.res
                      \de\
                         \strings.res
                      ...
        ...

Compressed file system

Field 8200 of TI-Nspire.img contains PK-Zipped files, used to setup the file system of the TI-Nspire. Its structure probably follows the target file system tree. The .tnc and .tno both have a phoenix/ directory, with a sub-directory for each module of the OS which contain localized resource files (.res), the 'getting started' .tnc file, and factory settings. The .tnc has a special directory ti84/ which contains an image of the TI-84 Plus archive memory splitted into 64kb files, used to setup the memory of the emulated TI-84 Plus. Some flash apps are preinstalled in this image.

The files in the sub-directory phoenix/ are the same between the TI-Nspire and the TI-Nspire CAS, excepted the sample document Getting Started, the .res files of ctlg (catalog) and syst (system), and the factory settings in factory.zip (the TI-Nspire is set to real for Real or Complex, the TI-Nspire is set to 4=??).

boot2.cer

Only present if the OS file contains an update of the boot 2.

Contains the field 340 with the same content as the one found in boot2.img and its signature field 240. The signature is validated using a key hard-coded inside BOOT2 (its modulus is EDBF3336...)

boot2.img

Only present if the OS file contains an update of the boot 2.

Structure:

8000

8040 : Product Name: 'BOOT2 '
8010 : ProductID '50C'
8010 : ProductID '50E'
8020 : Product ID '1.1.8981'|'1.4.1571'
8020 : Product ID (empty)
8080 : ??? 1180000000000001
0320 - 6 : Product Code: 0
8070 : Compressed contents

0240 - 128 - @TI-Nspire 1.4: 12FEC7. Signature of the field 8000, validated using the key given in boot2.cer (and again below.)

0340 - 146 : Identical to the field 340 of boot2.cer

:: 0270 - 1 : ??? \x00
0260 - 140 : [#1024-bit_RSA_public_keys|1024-bit RSA public key]] used for validating the first part of boot2.img

0240 - 128: Signature of the field 340. Does not depend on the content of the fields 8000 and 240 above (same between boot2 1.1 and 1.4), and different from field 240 of boot2.cer. This signature is validated using a key hard-coded inside BOOT1 (its modulus is CC14CF31...)

FFF0 - 0 : END_OF_CERT

1024-bit RSA public keys

These keys can be found in boot2.cer, boot2.img and TI-Nspire.cer, in the certificate field 340. They are formatted in ASN.1 DER format, as described here or here. As a bytes sequence, the format is: 

30 81 89 02 81 81 00 [128 bytes: the key] 02 03 01 00 01

The final 01 00 01 is the RSA exponent, which means 65537 in DER, a common value for e.

There are three of these keys known:

  • "boot" key: stored in boot2.cer and boot2.img, used to validate the first part of boot2.img
  • "OS" key: stored in TI-Nspire.cer, used to validate the OS
  • a second key stored in TI-Nspire.cer, purpose unknown

Signatures consist of a "0240" field of 128 bytes; raising this (big endian) number to 65537th power mod n gives a padded SHA256 hash of the data being signed.

The public key used by boot1 to validate boot2.img is embedded in boot1. The public key used to validate TI-Nspire.cer is embedded in boot2.

Boot1 validates the signature of boot2 at boot-time. Respectively Boot2 validates the signature of the OS at boot-time.

Breaking RSA : twists on naive algorithms

The Perl scripts below use a naive integer factoring method (trial division), with twists. An element of luck is added to the script.

  • The first script takes the square root of n (the key), to get an approximate value on a prime(p) , then decrement that value and see if it divides n. You continue with this until you get a hit. Two lines were added to the procedure: the starting value of p is bit shifted to the right by the hour of the GMTIME. So someone around the world running this might get extremely lucky and crack it in an hour !! The starting trial prime size for p can be anywhere between 489 bits and 512 bits, which is typical when you look at known key primes. For example, if a prime to a 1024 bit key is 498 bits, the person who gets the 498-499 bit value, might crack it in hours, the one who gets 497 bits would never crack it, the one who got 511 bit start value would crack it in millions of years.
  • The second script generates all 512-bit numbers, using a LFSR seeded with the current time.

The 3 keys discussed on this page (boot.cer,boot2.img,TI-Nspire.cer) are in these scripts - uncomment one of them in. You can test them with the 512 bit keys recently cracked on the other Ti calculators here. For general links to this controversy see (1), (2) and (3) on ticalc.org. The programs below are nevertheless extremely time intensive. 

 #!/usr/bin/perl
 # crackRSA.pl 
 # set your console window to 150 characters wide for progress output
 # old fashion brute force factor algorithm, with a little luck
 
 #use lib '../lib'; # uncomment this if you unzip Math::BigInt to a nonsystem directory	
 use warnings;
 use Math::BigInt try => 'GMP';  # faster if GMP installed, falls back to pure perl otherwise
 
 print "# Using Math::BigInt v",$Math::BigInt::VERSION,"\n";
 
 #  ---- public encryption key '$e'
 $e = Math::BigInt->new('65537');
 
 #  ---- modulus or second public 1024-bit key '$n' - uncomment in only one of three $n below
 # ---- boot2.cer & boot2.img keys(same number):
 #my $n = Math::BigInt->new('0xc3b3a7015c04299ff3a25f104e2285c1ec2d55471e6208959d0f6981b2fa2c6d3e316f9364d5eb5c7789e142b75bfaf402e7e02fac0cb09f6419db1f44679f8bbcca142f1d312feb095708ef175a4ef80271321e7240f0d854c90a74fc59209cdf80aa8f85ae3b948a3ce55c69cd050098d5a79aebbc241cc642b106b1af2cb7');
 # ----- TI-Nspire.cer, 2 keys:
 #my $n=Math::BigInt->new('0xaba7f0b8c7feb6e33438af5c25c67389eaf4d73f80cd0a37922493431cde03b34da448bdb05387cf7a8c59ee12d9613429a2b07ea385752f079892da1ae76c2b158f2d7169aae066432fe44f797df39dd6a0d7b2e2091281b30efac247c51576ebc93ec456de2e27d36b713844336b65af67ee58e6107a6a1deb954a91095295');
 #my $n=Math::BigInt->new('0xb15e01c47c421be62f4e769b3ac98f4f983a820b0c181e35715d84a4f1acf0527eeddfabf9f66e73bedb55376e22f860c34dc70ce239157297056d4ecf46535778c3917647b5a6bb9c5638cdeff3e309ff66878fd4f233cf157d7af4136f307df90ec6ae6eaff6bead6d52f423a37dac59ff38ae876008103728f2bd674e858f');
 
 # --- now brute force find factors ---
 $p = $n->copy();
 $p->bsqrt();   # ~ p
 $biggestp = length($p->as_bin())-2;
 print "prime p is a ",$biggestp," bit number or less.\n";
 $p = $p->brsft((gmtime(time))[2]);  # random right shift start on by which hour
 if((gmtime(time))[2] > 0){$p = Math::BigInt->new('0b' . ('1' x ($biggestp-(gmtime(time))[2]))); } # so no integers are missed by this scheme
 print "p randomly starts shifted right by ",(gmtime(time))[2]," bits and bit filled.\n";
 
 ITERATE:
 $modtest = $n->copy();
 if ($modtest->bmod($p)->is_zero()){
 print "Great found p and q !!!!!\n";
 print 'p= ',$p->as_hex(),"\n";
 $q = $n->copy();
 $q->bdiv($p);
 print 'q= ',$q->as_hex(),"\n";
 goto SECRETKEY;                   
 }
 
 DECREMENT:
 $p->bdec(); 
 goto DECREMENT unless $p->is_odd();
 print 'p=',$p->as_hex(),"\r";  # comment out for speed for serious cracking                                          
 goto ITERATE;
 
 SECRETKEY: # calculate private decryption key  'd' 
 print "Calculating secret key d\n";
 $PQ = $p->copy();
 $PQ->bdec();
 $r = $q->copy();
 $r->bdec();
 $PQ->bmul($r);   # $PQ = (p-1)(q-1)
 $d = $e->copy()->bmodinv($PQ);
 
 print 'p= ',$p->as_hex(),"\n";
 print 'q= ',$q->as_hex(),"\n";
 print 'd= ',$d->as_hex(),"\n";
 print 'n= ',$n->as_hex(),"\n";
 print 'e= ',$e->as_hex(),"\n";   
 

 #!/usr/bin/perl
 # crackRSA.pl
 # set your console window to 150 characters wide for progress output
 # old fashion brute force factor algorithm, with a little luck
 
 #use lib '../lib'; # uncomment this if you unzip Math::BigInt to a nonsystem directory
 use warnings;
 use Math::BigInt try => 'GMP';  # faster if GMP installed, falls back to pure perl otherwise
 
 print "# Using Math::BigInt v",$Math::BigInt::VERSION,"\n";
 
 #  ---- public encryption key '$e'
 $e = Math::BigInt->new('65537');
 $one = Math::BigInt->bone();
 # 512-bit Galois LFSR generator pattern
 $tap = Math::BigInt->new("0b101001001");
 $tap = $tap->blsft(Math::BigInt->new("503"));
 
 #  ---- modulus or second public 1024-bit key '$n' - uncomment in only one of three $n below
 # ---- boot2.cer & boot2.img keys(same number):
 #my $n = Math::BigInt->new('0xc3b3a7015c04299ff3a25f104e2285c1ec2d55471e6208959d0f6981b2fa2c6d3e316f9364d5eb5c7789e142b75bfaf402e7e02fac0cb09f6419db1f44679f8bbcca142f1d312feb095708ef175a4ef80271321e7240f0d854c90a74fc59209cdf80aa8f85ae3b948a3ce55c69cd050098d5a79aebbc241cc642b106b1af2cb7');
 # ----- TI-Nspire.cer, 2 keys:
 #my $n=Math::BigInt->new('0xaba7f0b8c7feb6e33438af5c25c67389eaf4d73f80cd0a37922493431cde03b34da448bdb05387cf7a8c59ee12d9613429a2b07ea385752f079892da1ae76c2b158f2d7169aae066432fe44f797df39dd6a0d7b2e2091281b30efac247c51576ebc93ec456de2e27d36b713844336b65af67ee58e6107a6a1deb954a91095295');
 #my $n=Math::BigInt->new('0xb15e01c47c421be62f4e769b3ac98f4f983a820b0c181e35715d84a4f1acf0527eeddfabf9f66e73bedb55376e22f860c34dc70ce239157297056d4ecf46535778c3917647b5a6bb9c5638cdeff3e309ff66878fd4f233cf157d7af4136f307df90ec6ae6eaff6bead6d52f423a37dac59ff38ae876008103728f2bd674e858f');
 
 # --- now brute force find factors ---
     $p = $n->copy();
     $p->bsqrt();   # ~ p
     $biggestp = length($p->as_bin())-2;
     print "prime p is a ",$biggestp," bit number or less.\n";
     print "Starting at ", time, "\n";
     $p = Math::BigInt->new(time);
     
     print 'p=',$p->as_hex(),"\r\n";
     $i = 0;
 
 DECREMENT:
     if ($p->is_odd()) {
         $p->brsft($one);
     }
     else {
         $p->brsft($one);
         $p->bxor($tap);
     }
 
 ITERATE:
     if ($i == 65535) {
         print 'p=',$p->as_hex(),"\r\n";
         $i = 0;
     }
     $modtest = $n->copy();
     if ($modtest->bmod($p)->is_zero()){
         print "Great found p and q !!!!!\n";
         print 'p= ',$p->as_hex(),"\n";
         $q = $n->copy();
         $q->bdiv($p);
         print 'q= ',$q->as_hex(),"\n";
         goto SECRETKEY;
     }
     $i++;
     goto DECREMENT;
 
 
 SECRETKEY: # calculate private decryption key  'd'
     print "Calculating secret key d\n";
     $PQ = $p->copy();
     $PQ->bdec();
     $r = $q->copy();
     $r->bdec();
     $PQ->bmul($r);   # $PQ = (p-1)(q-1)
     $d = $e->copy()->bmodinv($PQ);
 
     print 'p= ',$p->as_hex(),"\n";
     print 'q= ',$q->as_hex(),"\n";
     print 'd= ',$d->as_hex(),"\n";
     print 'n= ',$n->as_hex(),"\n";
     print 'e= ',$e->as_hex(),"\n";

We need your help

  • Find out what the unknown fields of TI-Nspire.cer and TI-Nspire.img mean
  • Help us to break the encryption of field 8070 in TI-Nspire.img
  • Find all the differences between the official release of the TI-84 Plus OS and the OS image used in the TI-Nspire for its emulator. But DON'T try to flash it to your TI-84 Plus. The TilEm emulator which worked perfectly with all real TI-84 Plus ROMs up to 2.43, just freezes with the 2.44 & 2.46 special Nspire ROM dumped with TiLP: this is because all Nspire 84+SE OSes contain invalid instructions (to perform emulator functions) which will lock any real calculator or emulator.
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