Day 9: Elliptic Curves

Resources (optional)

• lecture notes (Saba Eskandarian; Stanford CS 355, Spring 2021): Saba’s notes

Lecture Topics

• notes
• elliptic curves
  • hobbies in antiquity
  • finding rational points
  • constructing a group

Problems

Today, we’ll move away from Replit and program on our own computers.

You’ll see that the programs we’ve been writing (encryption, decryption, key generation, signatures, etc) can be used on your own files!

We’ll be working in the command prompt/terminal. You’ll need the following commands on Linux/Mac (windows in parentheses):

• ls (windows: dir): list files in current directory
• echo TEXT > FILE (windows: echo TEXT > FILE): write TEXT to FILE
• diff FILE1 FILE2 (windows: fc /B FILE1 FILE2): compare two files and print something if they differ
• cat FILE (windows: print FILE): print a file
• rm FILE (windows: del FILE): remove a file
• python3 FILE ARG1 ARG2 .. (windows: python3 FILE ARG1 ARG2 ..): run the python script FILE with arguments ARG1 ARG2 ...

You’ll be working in cryptotool.py. Download it here and put it on your desktop. You’ll be writing you code in the main function. Look for the # TODO comments.

These functions might be helpful:

• write_bytes_to_file(bytes, file): creates a new file and writes bytes to it
• read_bytes_from_file(file): read the contents of a file, as bytes
• any_object_to_bytes: formats any Python object as bytes
• any_object_from_bytes: the inverse of the above

Each problem today involves implementing a new subcommand for cryptotool.py that will allow it to do some cryptographic operation. Usually, the command will take command like arguments, and may read/write files.

For example, once you’ve implemented the keygen, enc, and dec subcommands, you should be able to run the following in your terminal:

python3 cryptotool.py keygen -k mykey # creates a new file 'mykey' with a random key
echo hi there > mymsg # creates a new file 'mymsg' with 'hi there'
python3 cryptotool.py enc -k mykey -m mymsg -c myciphertext # creates a new file 'myciphertext'
python3 cryptotool.py dec -k mykey -m mydecodedmsg -c myciphertext # creates a new file 'mydecodedmsg'
cat mydecodedmsg # prints out that message!

I recommend doing the problems in this order:

1. Symmetric key generation (required):
   • python3 cryptotool.py keygen -k FILE: generate a random symmetric key and store it in a file
     • use random_bytes
   • python3 cryptotool.py passwd-to-key -p PASSWORD -k FILE: hash a password to a key (and store it in a file)
     • encode the password as bytes using passwd.encode('ascii') and then hash it
2. Symmetric ciphers (required):
   • python3 cryptotool.py enc -k FILE -m FILE -c FILE: encrypt
   • python3 cryptotool.py dec -k FILE -m FILE -c FILE: decrypt
3. Decoding your secret message! (optional)
   • Each group has a message that I’ve encrypted to them using a password-derived key.
   • You can get your group’s password from me, when you’re ready.
   • The ciphertexts are here:
     • alligator
     • bumblebee
     • cat
     • dog
     • elephant
     • fish
     • giraffe
     • hippo
4. Public-Key encryption: (optional)
   • python3 cryptotool.py keygen -sk FILE -pk FILE: generate a keypair
   • python3 cryptotool.py enc -pk FILE -m FILE -c FILE: encrypt
   • python3 cryptotool.py dec -sk FILE -m FILE -c FILE: decrypt
   • now, try encrypting a message to yourself and then decrypting it!
5. Signatures: (optional)
   • python3 cryptotool.py sign -sk FILE -m FILE -s FILE: sign
   • python3 cryptotool.py verify -pk FILE -m FILE -s FILE: verify, prints ‘True’ or ‘False’
   • now, try creating a signatures and then checking it!

Fun things to do:

• Try encrypting some of your normal files (e.g. MS word files) and then decrypting them. Can you open the decrypted files?
• send a message to your group-mates using a password-derived key