Public-Key Cryptography and Key Exchange · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Split the secret, share half openly

Computing · Networks & Security · ages 20-22
Name ______________________   Date ____________

  1. What can the public half of a key pair do?

    • Unlock anything locked by anyone
    • Lock a message that only the private half unlocks
    • Replace the private half entirely

  2. The private half of a key pair is never revealed to anyone.

    Circle one:   True   False

  3. A pair (3, 4) is scrambled by [[1, 2], [0, 1]]. What is the first number of the new pair?

    Answer: ______________

  4. Maya scrambles a secret note by multiplying each pair of numbers by the matrix [[1, 2], [0, 1]]. To turn the scrambled note back into the real one, what do you multiply by?

    • The same matrix [[1, 2], [0, 1]] again
    • The undoing matrix [[1, -2], [0, 1]]
    • Any matrix that has the same numbers in it
    • Nothing can undo it

  5. Why do computers swap a symmetric key instead of carrying the chat on public-key methods?

    • Public-key methods are slower, so the fast cipher carries the talk
    • Symmetric keys cannot be swapped at all
    • Chats are too short for symmetric ciphers

  6. A note has the pair (3, 4). It is scrambled by multiplying with the matrix [[1, 2], [0, 1]], which gives a new pair. What is the first number of the new pair?

    Answer: ______________

  7. In this matrix secret-message method, if you publish the scrambling matrix for everyone to see, people can work out the undoing matrix from it, so this method cannot safely have one public half.

    Circle one:   True   False

  8. You publish the toy scrambling matrix for all to see. Why is there no safe public half?

    • Nobody can multiply matrices in public
    • Anyone can compute the undoing matrix from the published one
    • Published matrices stop working entirely

  9. A new pair (5, 1) is scrambled by [[1, 2], [0, 1]]. What is the first number of the result?

    • 5
    • 6
    • 7

  10. Two strangers exchange key messages while somebody records everything. What does the watcher end with?

    • The agreed secret, read straight from the recordings
    • Recorded messages but nothing that reveals the secret
    • Nothing at all, the line goes silent
LightMySky · lightmysky.comW1-mt_AHCtrer4eh-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Split the secret, share half openly W1-mt_AHCtrer4eh-s1

  1. Lock a message that only the private half unlocks · Locking is public, unlocking stays private to the key owner.
  2. True · Publishing it would hand every reader the power to unlock.
  3. 11 · First row gives 1 times 3 plus 2 times 4, which is 11.
  4. The undoing matrix [[1, -2], [0, 1]] · Scrambling with a matrix is undone only by its inverse matrix, the matching half that reverses the first half.
  5. Public-key methods are slower, so the fast cipher carries the talk · Public-key sets up the secret, then the fast shared key does the heavy lifting.
  6. 11 · Multiplying (3, 4) by [[1, 2], [0, 1]] gives (1*3 + 2*4, 0*3 + 1*4) = (11, 4), so the first number is 11.
  7. True · True. Anyone who knows the scrambling matrix can compute its inverse with a short formula, so both halves leak at once. Real public-key systems use math where the undo half stays hidden even when the scramble half is published.
  8. Anyone can compute the undoing matrix from the published one · Both halves leak at once here, unlike real systems where the undo half stays hidden.
  9. 7 · First row gives 1 times 5 plus 2 times 1, which is 7.
  10. Recorded messages but nothing that reveals the secret · Overhearing every message still yields no usable secret when the math holds.
Worksheet · LightMySky