# Due Wednesday, September 30th

Due Wed:

• Module 1 Solutions are here.  I know many of you are curious about the tricky counting problem!
• To Know:  My plan is to post the Module 2 assessment on Wednesday, with one week to do it.
• To Know:  If you’re interested in the runtime of the Index Calculus, here are some course notes that cover it in more detail (from Andrew Sutherland’s MIT course on elliptic curves).  This may be an interesting topic for a graduate student project:  runtime for index calculus and/or index calculus improvements mod p and/or in other finite fields.
• FOR GRADUATE STUDENTS:  Please provide me by Friday (email is fine) a short paragraph description of what you intend to do for your written project for the course.
• To Do:  El Gamal Encryption Chain!  Check out the El Gamal Tools.  We will use the prime there (the next prime after 10^6), and the primitive root 2.  This is set up on that tools page.  Here are my notes from class on El Gamal; you’ll also find it in Section 7.5 of the 2nd edition of the text on canvas.  Do the following:
• Set up a private and public key for yourself.  Publish the public key on the “#ciphertexts” channel on discord (Under Study Groups).  Note your public and private key down on paper.
• Choose a four-letter word as a message.  It should be a polite, recognizable english word, so the decrypter will be able to tell they’ve done this correctly.  It should answer, in some fashion, the question “What do you like?”  Make notes on paper.
• Find the most recent unused public key on there (if possible), and use the public key to encrypt your four-letter word to that person. (It will involve two chunks, so you will have to send them as two separate ciphertexts.)  Keep notes on paper of the key steps.
• Post your ciphertexts publicly for that person on the channel.  Since it consists of two chunks, you should post two pairs (r,t).
• When you receive a message from someone on the channel, decrypt it.  Hopefully it is an english word.  If it is, yay!  Respond on the channel to that person to tell them the decryption you got.  Keep notes on paper of the key steps.
• For the canvas submission, show your notes from this work.  If you don’t get someone sending you a message in time, that’s ok, but keep an eye out and do the decryption stage when possible.