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Sada and her fried Nadine found a novus text. They think the person who wrote it was trying to convey some message.

Just before the text was a bit of mathematics but their knowledge on mathematics is not so great. So they decided to rely on their friend Aaron.

...
f(x) € Z, -5^35 <= f(x) <= 3^37
∴ P(f(x1) = f(x2)) ~ 0 
Q.E.D

f(Wrna-Ybhc Tnvyyl naq Znex Nqyr) = 1964029968

H4sIAAAAAAAA/8VYW24DIQz8zyl6BB4Gw/0vViItY6rxItI06l+0PDzY47GdkiT1Gr4etcXSpI0fuWho/euhJVctZXypsaes40tQ7b2uP2rVltbNKXSNTdYlOmUmouSS8/gircU6fmhSqeFpSzSmOPBolhBFVhhzCbZ4yUzUkFJP3uYBOOQY1+O0mTEb1Pu370zMzbDFDk+t5Zr8B06jtiQp1fREOHDlVtYvODV2B31GuZSsIazgZwgcWwTV3DKDYg4nHwIP28rjsIb1wlJzje3HKc05V5ctJ57HHrsQz8E9k2xwiz0Q5EfcEUp71/VS58kbYIgFNiMEFHdstryYX+xmumeTMnipseWE/Ng8ncDZDUc5PoSJA4ReKC9gDm0k96JrfnEoHWAIgVkPZSjgSpu5tOBpoupiNh2jKC8koYzjNGdtgQlLxo3kki1W0XuK2ikwgQk5s9KRd2gC3cNqzO41IiGU5g161wS/oQRvdlhHwujIBdHYMDNtThSgVRFxKYon8xIzysGD6EAuuFLDmfDGfa10lA0em1BNHLi4EGYnXuhA7tuMTVo51eokl6nb4TLqsJesm6Ooppjk0s1OwmIz049DcPBAR3tJ9E7ya6PGOzl980LIKTzPTCA9tFAil0n5TcO5BaWbT9LzTcl9s1F0silIzfLDGxRuhxLcgm6KAqnNhmOOiZeaJW5BuWhSuNnzyMEjQjLZflffmc8HCfLPFW0TbkeNL61j2WGoXC+cBNk0HugueELc9OFYolMv1WUHz19XRufmV+ZuhzYxxtb8Vu2+af/gOMmja5fak5sFHLhfzu+4kDsinm6YopSnTlpNb3xuqnUoQZPUjuF/pZCUuU6+b4bZk1IChNwRbfxDM/VC46vT21RzZ+yCe+l/AGcApwvBhG9K427FXxMAAA==

Can you find out the text that Aaron was able to decipher due to his ancestry?

(Sorry I've ciphered the wrong text on my first version)

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The top message

P(f(x1) = f(x2)) ~ 0 means "it is highly unlikely that no two inputs give the same output". Coupled with the large range given (accidentally using € instead of ∈), this makes it likely that f is a hash function. However, the given output does not match any common hashes. I'm not sure how this is relevant.

Step 1

Decoding as base64 gives a .zip file. (This was hinted at by Wrna-Ybhc Tnvyyl naq Znex Nqyr, which is rot-13 of Jean-Loup Gailly and Mark Adle: two inventors of gzip.)

Step 2

This zip file has a single other file inside it with no extension: interpreting as .txt gives the following numbers: enter image description here

(Here are the numbers in Pastebin for convenience's sake.)
As M Oehm noticed, each of these in hexadecimal has the form 0xYZ00YZ, where YZ is a hex code for a printable ASCII character. These characters spell out the final answer, a Lorem Ipsum variant:
Phasellus ullamcorper erat eget lacus egestas, eu bibendum est pretium. Vivamus euismod sagittis enim, non imperdiet ligula semper et. Sed a neque fermentum, cursus turpis ut, vulputate lectus. Suspendisse quis ex ac ante volutpat tincidunt. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Maecenas ut venenatis est, dapibus elementum metus. Suspendisse ut leo suscipit, porttitor ex a, tincidunt tellus. Nulla bibendum eu justo eget sollicitudin. Vivamus tempor dapibus ipsum, ut varius nibh accumsan ac.

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  • $\begingroup$ Good job. All I am going to say converting the numbers to ASCII is not necessary. Can you say anything about the text that was hashed? $\endgroup$ – Bruno Costa Feb 9 '18 at 6:35
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    $\begingroup$ All of these numbers are 6-digit hexadecimal digits of the form #xy00xy, where xy is the ASCII code of a printable character. Decoding just x % 256 for each number x yields a text that looks like a close couisin of Lorem Ipsum. (And given the OP's comment above, it probably just means as much.) $\endgroup$ – M Oehm Feb 9 '18 at 6:38
  • $\begingroup$ @M Oehm. Impressive you might as well give an answer although it would be nice to find what other clues I gave in my puzzle that the text could actually be an excerpt of Lorem Ipsum. And even the paragraph that was used. $\endgroup$ – Bruno Costa Feb 9 '18 at 7:22
  • $\begingroup$ @MOehm Ah, duh. I'm not sure how I missed that. $\endgroup$ – Deusovi Feb 9 '18 at 7:33
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@Deusovi and @MOehm correctly found the answer but they have missed some clues on my puzzle.

Sada, Nadine and Aaron are Latin names. Novus and the mathematical Q.E.D are also Latin. This should have been enough proof there was something about latim in the puzzle. Probably the original text.

Without no further clues one can only guess I was talking about a famous latim text such as "Lorem Ipsum".

The hash function that was used to hash Wrna-Ybhc Tnvyyl naq Znex Nqyr was string.GetHashCode from c#. the idea was you would use char.GetHashcode to map all alphabet letters into the numbers. Otherwise chat.GetHashCode is not hard to discover as @MOehm shown.

There were also two references to the number 13 in 5^35 <= f(x) <= 3^37 as 5+3+5=13 and 3+3+7=13. This was both the key to use in the ROT and the paragraph number from Lorem Ipsum.

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