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This forum is meant for discussing and sharing ideas of the Level II challenges. Do not post any complete solutions or codewords for any of the challenges. In case of posting solutions your post will be deleted and your account will be banned immediately.



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 Post subject: Challenge "Not-so-Secret Message from Malawi — Part II (ECC)"
PostPosted: Sat May 15, 2010 13:08 
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Joined: Wed Sep 30, 2009 14:10
Posts: 180
It is also important to choose the parameters of an elliptic curve cryptosystem wisely. This was not done in this example, which should enable you to decrypt another ciphertext message from Malawi. The plaintext reveals the codeword, although this time it is not as closely related to the photo.
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Last edited by admin on Wed Jul 31, 2013 15:14, edited 1 time in total.

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 Post subject: Re: Challenge "Not-so-Secret Message from Malawi – Part II"
PostPosted: Wed Jul 27, 2011 16:31 

Joined: Sat Jun 18, 2011 13:43
Posts: 149
Something is really messed up with this "elliptic curve". I have no idea how I am supposed to use this to my advantage.


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 Post subject: Re: Challenge "Not-so-Secret Message from Malawi – Part II"
PostPosted: Thu Jul 28, 2011 12:58 

Joined: Sat Jun 18, 2011 13:43
Posts: 149
Yes, yes...YESSSSSSSS. I've done it!


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 Post subject: Re: Challenge "Not-so-Secret Message from Malawi – Part II"
PostPosted: Thu Jul 28, 2011 14:54 

Joined: Sat Jun 18, 2011 13:43
Posts: 149
Ok, I guess I had a problem with this because I knew too much theory (I am a number theorist with a very tiny knowledge of programming, hence why I find it very difficult to solve most of the level 2 problems).

The curve given is NOT an elliptic curve modulo the prime that is given (we have bad reduction). This is the weakness.

Fortunately the non-singular part of this curve mod p DOES have a group law attatched to it and this group law is much simpler to work with. The discrete logarithm problem is simple to solve on this curve (although I had to search for mathematical patterns).

I did this without having to program a single thing!


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 Post subject: Re: Challenge "Not-so-Secret Message from Malawi – Part II"
PostPosted: Thu Jul 28, 2011 21:49 

Joined: Sat Jun 18, 2011 13:43
Posts: 149
I actually have a second solution to this too, one that makes this even easier to solve but is harder to come up with and requires specialist mathematics.


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 Post subject: Re: Challenge
PostPosted: Wed Jan 08, 2014 20:47 

Joined: Sat Dec 14, 2013 19:26
Posts: 11
Hi,

I find that the discriminant is zero (mod p).
So E is singular.
I also find that c4 = 0 (mod p), so the curve has a cusp...

After I'll have to find the map of the isomorphism between E and the underlying (additive, as I have c4=0) group of Fp.


am I on the right way ?

Many thanks for your advice.


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 Post subject: Re: Challenge
PostPosted: Thu Jan 09, 2014 18:34 

Joined: Sat Dec 14, 2013 19:26
Posts: 11
forget about my question, it's OK a got it...


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