TEST WEDNESDAY (see Tests tab for syllabus/review)

POSTER GROUPS. Ok, at this point if you haven’t gotten an email from me, then I think you’re working out a group of your own, but if that’s not the case, let me know! Get going looking into cool topics! Click “Posters” tab above.

Use the Miller-Rabin primality test with a=2 to determine if $n=90751$ is composite or probably prime. Show your steps.

If it comes up probably prime, try it with a=3. Show your steps.

Next, possibly using the Miller-Rabin Tools, implement the Miller-Rabin primality test to test if n = 3057601 is composite or probably prime, using the base 99908.

The euler-phi function gives: phi(21733) = 21420. Use this fact to factor 21733. (Hint: revisit notes in class friday sept 27, I explained how to use a quadratic formula to do this).

Factor $n=31861$ using the Quadratic Sieve Tools page to produce the relations you will need. You may need to expand your factor base or the number of relations the boxes produce.

If you got lucky and got a single relation that did it, can you instead find a pair or larger combination of relations that do it?

Many of the messages posted on the #ciphertexts channel during the RSA ciphertext chain were pretty small. Can you attack any of them using the “small message” attack demonstrated in class?