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Challenge "Smartcard RSA"  

  By: admin on Oct. 25, 2010, 4:57 p.m.

To achieve a very fast decryption in RSA, one might choose the secret key to be rather small. It should, however, not be too small, since then it might be possible to mount brute-force attacks. The same holds for variants like RSA-CRT.
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 Last edited by: admin on Oct. 31, 2021, 2:54 a.m., edited 1 time in total.

Re: Challenge "Smartcard RSA"  

  By: parin.shah on March 21, 2011, 10:37 a.m.

Can anybody provide some hint regarding the challenge..!!

Re: Challenge "Smartcard RSA"  

  By: mazze on March 29, 2011, 8:43 a.m.

Do as the challenge text suggests. Look at RSA-CRT and try a brute force attack.

If you ask a more specific question you might get a more specific answer.

Re: Challenge "Smartcard RSA"  

  By: Veselovský on July 31, 2011, 1:24 a.m.

How much are "dp" and "dq" small? Bellow 10, 1000 or 1000000?

Re: Challenge "Smartcard RSA"  

  By: DarkFibre on Aug. 10, 2011, 12:55 a.m.

Is there someone I can ask if I'm on the right track, or just wasting computing cycles?

Re: Challenge "Smartcard RSA"  

  By: mazze on Aug. 10, 2011, 8:52 a.m.

I am not sure how large d_p and d_q are exactly,but the actual problem is to find out how to verify, if a certain guess is correct. Once you know how to check,it should be no problem to mount the brute force attack. If you implement it correctly, then the attack should take a reasonable amount of time. Depending on your programming skills, programming language and computing power, I would guess it takes something between 10 seconds and 5 hours …

This forum will provide help with solving a challenge,if you ask a specific question, i.e. no questions like "I don't know what to do, please help".

Re: Challenge "Smartcard RSA"  

  By: mazze on Aug. 11, 2011, 11:23 a.m.

A good idea to check if your idea is correct is to construct a small example yourself.

Re: Challenge "Smartcard RSA"  

  By: fretty on Aug. 14, 2011, 11:47 a.m.

I have been looking into this and I am not sure what direction to take.

Am I right in thinking I need to use lattices here or is that going too far?

Re: Challenge "Smartcard RSA"  

  By: Flip on Aug. 18, 2011, 11:10 a.m.

How do you translate between words and the integers mod N?

Re: Challenge "Smartcard RSA"  

  By: fretty on Aug. 18, 2011, 11:20 a.m.

What do you mean?

Re: Challenge "Smartcard RSA"  

  By: Flip on Aug. 18, 2011, 12:05 p.m.

Oh, I see. Please disregard my question. [HTML_REMOVED]

Re: Challenge "Smartcard RSA"  

  By: fretty on Aug. 18, 2011, 12:40 p.m.

Since you solved this…near enough immediately…can you give a hint, pretty please? :p

Re: Challenge "Smartcard RSA"  

  By: Veselovský on Aug. 18, 2011, 5:37 p.m.

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I have solved it by myself now, but had to reading almost every publication that is available on the net on the topic RSA…
hmmmm… although I do not fully understand, why it works…

Re: Challenge "Smartcard RSA"  

  By: Veselovský on Aug. 18, 2011, 6:32 p.m.

I have to correct my previous post slightly…
I fully understand the attack I have done, but there were more complicated attacks effective for even bigger d_p and d_q than in challenge… and these are that I do not fully understand

Re: Challenge "Smartcard RSA"  

  By: h3po on Aug. 21, 2011, 4:40 a.m.

i can't for the life of me find any information on how to solve the equations that i get from the construction of y to verify my bruteforce. every single paper i read (8 so far) throws complexity optimizations with lettuce mathematics at me, which i don't understand and most probably don't need to solve this. can someone please point me in the right direction?


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