Noise in the Air

Josh Marron, Jay Pottharst

SOLUTION:

The first task is to crack the encrypted files. Assuming you're a little bit familiar with how RSA works (or, is implemented in openssl), here is a sketch of the steps.

First file. The numbers, and the steps to get them, are

• modulus in hex: 343ee3cb31fdf5654a605fadac83 ("openssl rsa")
• modulus in decimal: 1059667944211022744608930637130883 (any large integer program)
• factorization of modulus: 30016394643021617 * 35302972152832499 (your favorite fast numerical program
• public exponent: 65537 (default)
• private exponent: 740265460576670450675406279585185 (use euclidean algorithm, large integer program)
• coefficient: 2667138270473137 (ditto)
One can either directly attempt to use these to decrypt the .bin files, or make a sample 110-bit .pem file and overwrite its bytes with (the hex of) the data above. Using the resulting 1private.pem file together with "openssl rsautl", one gets:
These give "exponentiate".

Second file. Only the numbers this time.

• modulus in decimal: 39285388713983789308503556506560761019385342151493316661
• factorization: 4443374022970521144915212423 * 8841341852136137841331063907
• public exponent: 65537 (default)
• private exponent: 24333598874764757971670863364024105109889815896517056857
• coefficient: 4035184019340517077671806892
Overwriting a sample 185-bit key with all this to get 2private.pem (say), and using this to decrypt, we get:
For a total of "position index by".

Third file. Make sure you got a very good factorization program.

• modulus: 39033433635675101519702166311870912573685534868219440838838825063767
• factorization: 4646042589614472877897884108809489 * 8401436896624334067497275688137703
• public exponent: 65537 (default)
• private exponent: 6782622674871722173831091901667543583081838988537001970072123719297
• coefficient: 5443948948096410348483094060479906
Same with a 225-bit key to get 3private.pem, and decrypting gives:

So... you have been instructed to "exponentiate position index by 2003". So make a new file, where we take each ith character of noise.txt, and put it in the i2003th position of the new file. The resulting file has size 180991 = 241 * 751 (both prime), so there are only two ways to make the text into rectangles. One of these makes the text into a large "bitmap" of a turtle.