## Mon Oct 17 11:56:58 EEST 2011

### $abc$ triples

Got two lucky numbers from the math lottery.
High merit $abc$ triples related to the $abc$ conjecture $$11^{30}+3^{15} \cdot 13^{2} \cdot 19^{2} \cdot 41 \cdot 137 \cdot 233^{2} \cdot 44203^{2} \cdot 4758269=2^{54} \cdot 5^{8} \cdot 7^{2} \cdot 43^{4} \cdot 1451^{2}$$ $$2^{29} \cdot 5^{4} \cdot 7 \cdot 11^{15} \cdot 43^{2} \cdot 1451 + 13^{4} \cdot 44203^{4} \cdot 4758269^{2} = 3^{30} \cdot 19^{4} \cdot 41^{2} \cdot 137^{2} \cdot 233^{4}$$ Merits $24.2$ and $24.21$

Posted by joro | Permanent link

## Wed Oct 5 12:19:32 EEST 2011

### bug stories


i got involved in a bug in a major linux distro compromising their
update system if one can do "man in the middle" (e.g. DNS).

the bug had strange story. i forgot to pay the internet monthly bill.
the isp stopped my net, redirecting all pages to them telling
me to pay.

before the internet got working, i got local mail from cron
about apt-key not being able to import the html page as a key.
this drew my attention to the brain damaged part of apt-key.
the rest of the exploit was pure triviality.

another bug with a strange story was an openssl |use after free|.
i was generating rsa keys with another program.
imported in openssl a test key using middle clicking with the mouse.
unfortunately, i have failed to select a few digits of the number,
making a prime a composite (if the prime stayed prime the story would
have been different). basically this broke the math.
in addition openssl crashed, which was a bug.
it took some time to openssl developers to realize i didn't mind the
broken math but the crash.

a coincidence about several other bugs is they were found while
drinking coffee and smoking. no computer in the room, just relaxing.
suddenly i think of something i have read today and i find it quite
suspicious. leave the coffee and go to check. almost every time
i wasn't wrong about the suspicion.

certainly the majority of bugs were black labour (i don't think
|grep -rniI stuff *| is dead, though the prevailing opinion appears
different).

disclaimer: this is not a tutorial :)))


Posted by joro | Permanent link