05 · No trapdoor
Hash
A one-way function with no secret factors. Flip a letter, the digest jumps. Grover searches preimages in √N. Shor does not apply.
In English
A hash turns any message into a short fingerprint. Change one letter, the fingerprint should look unrelated (avalanche). There is no secret d to invert it — that is the point. Grover can search fingerprints faster, which means “use a longer hash,” not “hashes are dead.”
- Try this
- Click cat, then car. Watch the 8 bits jump. That jump is the wish SHA-256 grants at 256 bits.
- Keep this
- Hashes are one-way with no trapdoor. Grover nicks them; Shor does not.
Lab · flip a letter, wreck the digest
A toy 8-bit hash (djb2-ish). Not SHA. The move that matters: a tiny edit, a different looking string of bits.
H(“cat”) = 253 · 11111101
previous “cat” → 11111101
A cryptographic hash is one-way, collision-resistant, and mixing. This lab is an 8-bit toy so you can see the bits jump. SHA-256 is the same wish at 256 bits.
No trapdoor: there is no φ(n) to hide. Grover gives a square-root preimage search. That is a longer hash, not a funeral.