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Challenge "Summer Job"

Challenge "Summer Job"  

  By: admin on June 12, 2018, 1:16 p.m.

During your summer job in an Austrian weekly magazine a mysterious letter arrives. Are you able to decrypt the message?
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 Last edited by: admin on Oct. 31, 2021, 2:55 a.m., edited 3 times in total.

Re: Challenge  

  By: Sgt. Pepper on June 14, 2018, 2:16 p.m.

I'm pretty sure I got the right d and recovered m (I checked m^e mod n == c), but I'm unable to convert m to ascii text. All standard bin-to-ascii conversions, with and without padding etc., only return gibberish. I would be thankful for any hints…

Re: Challenge  

  By: AnLeRo on June 14, 2018, 8:45 p.m.

Hi,

you should convert your "m" to base 128 first, then to binary and then to ascii.

I hope this helps,
Anna

Re: Challenge  

  By: Sgt. Pepper on June 14, 2018, 10:40 p.m.

Yes, it did, thank you!

Re: Challenge  

  By: plexor on July 15, 2018, 12:46 p.m.

Hi!

I found two primes p and q such that p*q=n and then I've calculated phi(n). The public exponent from the problem (e=65535) doesn't have an inverse modulo phi(n). Are you sure 65535 is the right public exponent or it is 65537?

Thank you!

Re: Challenge  

  By: AnLeRo on July 17, 2018, 3:52 p.m.

Hi plexor,

I'm sure 65535 is the right public exponent.

If you want me to check your primes, please feel free to send me a PM.

Best wishes,
Anna

Re: Challenge  

  By: Bart13 on July 16, 2019, 5:40 a.m.

Once again, a challenge where it is more difficult to enter the intended solution than to solve the challenge itself!

We find a solution and then have to omit punctuation, convert to uppercase, but keep the spaces between the words and finally have to include padding (!) in the plaintext.
That makes for a lot of trial and error to finally get the green light, provided that you don't run out of trials before that.

Why not simply use the decrypt as the solution?
That can't be too difficult to check, can it?

Re: Challenge  

  By: Polaris on Aug. 9, 2020, 5:26 p.m.

Hello everybody,

Hi!

I found two primes p and q such that p*q=n and then I've calculated phi(n). The public exponent from the problem (e=65535) doesn't have an inverse modulo phi(n). Are you sure 65535 is the right public exponent or it is 65537?

Thank you!

Same here as for plexor. e=65535 gives with my primes p and q a negative d, which leads to nowhere.

On the other hand, 65537 gives a positive d and m, that satisfy c = m ^ d mod n (with the c from the pdf). Looks self consistent for me, but not for the original e. Are you really sure about e=65535? Or did I miss something?

And further:

What is meant by

…you should convert your "m" to base 128 first, then to binary and then to ascii. …

? There are several possibilites to do this (e. g. converting to binary, then grouping seven-bits-wise starting with MSB or LSB, or something completely different). Is there any additional hint?

Thanks in advance

Polaris

Re: Challenge  

  By: tryone144 on Aug. 9, 2020, 8:23 p.m.

Hi Polaris,

[SNIP]
Same here as for plexor. e=65535 gives with my primes p and q a negative d, which leads to nowhere.

On the other hand, 65537 gives a positive d and m, that satisfy c = m ^ d mod n (with the c from the pdf). Looks self consistent for me, but not for the original e. Are you really sure about e=65535? Or did I miss something?

65535 is indeed the correct e. Given the correct primes p and q, there is a (positive) d that satisfies e * d = 1 mod phi(n).
Feel free to send me a PM with your primes and I'll check them.

What is meant by

…you should convert your "m" to base 128 first, then to binary and then to ascii. …

? There are several possibilites to do this (e. g. converting to binary, then grouping seven-bits-wise starting with MSB or LSB, or something completely different). Is there any additional hint?
[SNIP]

The encoding of the message is seven-bit ASCII (not 8 bits). It should be sufficient to group the binary representation into 7-bit groups and decode them as ASCII characters.

Greetings, Bernd

Re: Challenge  

  By: Polaris on Aug. 10, 2020, 1:10 a.m.

Hi tyrone144,

thank you! Indeed 65535 is correct.

Polaris


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