Why a quantum computer stops at a lattice

Shor’s algorithm eats RSA in one move. The same machine gets almost nothing on a grid of points with a little noise added. One slider shows the difference.

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Tap a part of the diagram to open that stage.

What actually changed

RSA hid its secret inside a question a quantum computer turns out to be able to ask. Lattices hide it inside a question that stays exponential for both kinds of machine — while the owner of a short basis skips the question altogether.

What's inside

  1. 1 Factoring stops being hard — Nothing was wrong with the mathematics. The hardness was simply living in the wrong place.
  2. 2 Points instead of numbers — The lattice itself is public. Everybody can see the points.
  3. 3 The message is a point, then it is nudged — The noise is small enough to be undone and large enough to hide which point you started from.
  4. 4 Finding the nearest point is the whole problem — Known quantum algorithms shave the exponent on this problem. They do not remove it.
  5. 5 With the right basis it is one rounding — The secret is not the lattice. It is a good description of the lattice.

Explorable Explanations

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