For Wed Oct 26, 2022:

For Wed:

  1. Don’t forget the Module 4 Assessment is on Friday.  Calculators allowed like last time.  Details about the material (and review problems) are on the “Goals” page on the navbar above.
  2. To Do:  An Elliptic Curve El Gamal Ciphertext Chain!  Today’s question:  what did you miss during the pandemic?  You will encrypt your answer.  Here are the steps:
      1. Keep notes as you do all this.
      2. Here are the EC El Gamal Tools you can use to do this.
      3. As a group, we will all use the elliptic curve E given by $y^2 = x^3 + x^2 + x + 1$ over the finite field of p = 123456789101234567891027
        elements.  Note that $p$ is 3 mod 4.  We will furthermore use the point P = [3,11655832467975276266127,1] on $E$, which has order 61728394550949287614731.
      4. You should create a private and public key pair based on the information given above.  Publish your public key on the #ciphertexts channel on discord.  Keep your private key in a text document somewhere to use for decrypting later.
      5. You should answer the question (What do you miss during the pandemic?) with a word of 6 or fewer letters.  Translate this to an integer and add three digits of “padding” as explained in class.
      6. Turn your message into a point on the elliptic curve as described in class.
      7. You should then obtain the most recent public key on the #ciphertexts channel, and encrypt your ASCII message (turned into a point on the curve) to that public key.  Post your encryption to the channel, mentioning the  owner of the public key it is encrypted to.
      8. You should then keep an eye on the channel and when someone encrypts a message to your public key (they should mention you), you should decrypt it and announce what that person misses during the pandemic, mentioning them.
      9. When someone decrypts your message, you should give them a thumbs up to let them know it’s right (or let them know if it isn’t).
      10. Hand in your notes from this exercise to the canvas dropbox.