Spark & Anvil Privacy

Teach & case

Help a near-peer reason through the idea — when you explain it, you understand it best — then read the real decision it comes from.

A case · you decide

Ivo's 'secret' club cipher

Ivo — a student whose club wants to encrypt its messages so a rival club can't read them

The idea in play: a small keyspace is not security — a 25-shift Caesar cipher is trivially brute-forced.

Ivo's club picks a Caesar cipher — shift every letter by a secret number — and feels safe: "The rival would have to guess our secret shift!" Ivo does the math on how many secrets there actually are.

A Caesar shift can only be 1 through 25 (shift 0 or 26 changes nothing). That's the ENTIRE set of keys — 25 possibilities.

A rival doesn't need to be clever: try all 25 shifts, and read whichever one turns into English. On a phone that's seconds. The "secret" has nowhere to hide.

The club says "but they'd have to GUESS the shift." Does keeping the shift secret make it secure?

Someone suggests: keep the Caesar cipher but ALSO keep the whole method secret ("security through obscurity"). Safe now?

Brute-force a cipher yourself →

When two ideas meet: 2 cases with two people

A case · you decide

Cassia and Freya: cracking a shift

Cassia & Freya — a student who writes shift ciphers, and a friend who breaks them by counting letters

The idea in play: a shift cipher keeps every letter’s frequency, so the most common ciphertext letter usually stands for E and gives away the shift.

Cassia hands Freya a page of shifted English. The letter that appears most often is H.

In ordinary English text, E is the most common letter.

What shift should Freya try first?

Open the Cipher Lab →

A case · you decide

Mox, Pax and Sela: a secret made in public

Mox & Pax & Sela — a student of clock arithmetic, and two friends agreeing a secret over an open channel

The idea in play: in Diffie-Hellman key exchange, each side raises a public base to a private power modulo a prime, and both reach the same shared number that an eavesdropper cannot easily compute.

Everyone can see the prime 23 and the base 5. Pax picks a private 6 and sends 5⁶ mod 23 = 8. Sela picks a private 15 and sends 5¹⁵ mod 23 = 19.

Pax raises Sela's 19 to his private 6. Sela raises Pax's 8 to her private 15. Mox checks both sums on the clock.

What number do Pax and Sela each end up with?

Open the Cipher Lab →