Shor’s algorithm, explained

Why a quantum computer breaks today’s key exchange. And why it can’t break PacketLoq.

In 1994, Peter Shor showed that a large enough quantum computer could break the math behind the key exchanges many networks still use today.1

The short version

Shor breaks the math that lets strangers agree on a secret in public. Your sites aren’t strangers, so PacketLoq doesn’t use that math.

Spoiler: a large quantum computer could break today’s key exchange in under a week. PacketLoq’s keys would take hundreds of billions of times the age of the universe. See the numbers →

Or take the three-minute lesson ↓

Part one · The problem

Part two · Why PacketLoq is different

Step 1

Today’s key exchange is a one-way street

IPsec and TLS sessions start with public-key math, often RSA, Diffie‑Hellman or elliptic curves. It rests on a problem that’s easy one way and brutally hard the other. Multiplying two primes is instant; working back from the answer would take today’s computers longer than the age of the universe.

That one-way street is what lets two strangers agree on a secret while everyone listens.

Small numbers make the idea easy to see. Real RSA keys use a number 617 digits long, so the hard direction is out of reach for any ordinary computer.

Step 2

A quantum computer isn’t just faster. It’s good at one strange thing.

A quantum computer won’t speed up your spreadsheet. What it does unusually well is find a hidden rhythm: how often a very long sequence repeats itself. An ordinary computer has to walk the sequence step by step, and for real keys that walk never ends.

Take 7, 7², 7³ and so on, and keep the remainder after dividing by 15. The pattern repeats every four steps. Here the rhythm is easy to spot; in a real key, it’s longer than any ordinary computer could ever walk.

Step 3

Shor’s insight: the hard direction is a rhythm problem

Shor proved the hard direction can be turned into a rhythm problem. Find the rhythm, and simple arithmetic hands you the secret numbers. The picture shows the whole trick on 15; a quantum computer does the same on a 617-digit number.

The quantum computer does only the first box. Everything after it is arithmetic a phone could do.

Step 4

Why that breaks a recorded IPsec or TLS link

Shor’s method breaks RSA, Diffie‑Hellman and elliptic curves alike, and many IPsec and TLS sessions still open with one of them, in the open. Record it today, and a future quantum computer recovers the session key. Every packet after it opens. Hardware estimates keep moving that day closer.2

Break the key exchange, and every packet after opens. The attacker only needs the recording and patience.

Step 5

What Shor can’t touch: a plain secret key

The data itself is encrypted with a symmetric cipher like AES‑256: one shared key of 256 random bits. There’s no rhythm in it for Shor to find.

The best quantum attack, Grover’s algorithm,3 only speeds up guessing, to about the square root of the tries. For AES‑256 that’s still around 2¹²⁸ steps, which is why cryptographers and the NSA keep it.4–5

So why not just use AES‑256? You already do: IPsec and TLS encrypt your data with it. The weak point is how both ends agree on the AES key, through an exchange Shor can break. PacketLoq keeps AES‑256 and removes the exchange.

Picture every possible AES‑256 key as the area of a square. An ordinary computer has to search the whole square. A quantum computer running Grover only has to walk one side, but that’s still about 340 trillion trillion trillion steps. Out of reach.

Step 6

Where PacketLoq fits: nothing on the wire for Shor

PacketLoq doesn’t open its links with a public-key exchange. The key is placed at both ends in advance, session keys stay inside the encrypted link, and they rotate on their own.

A recording holds only symmetric ciphertext: nothing for Shor, and AES‑256’s full margin against Grover.

Patent pending · US · Canada · EU

Step 7

The honest part: the question moves to the keys

Removing the key exchange moves the question from “can the math be broken?” to “who can get at the keys?” That’s why PacketLoq is built around key custody you can prove to an auditor.

Encrypted key vaultKeys are stored encrypted on the box.

Crypto ignition keyA physical key that has to be present to unlock the stored keys.

Three-pass zeroizeDestroyed keys are gone for good.

Full audit logWho touched which key, and when.

Step 1 of 7

The bottom line · How long would it take?

Same attacker, same quantum computer. Very different outcomes.

Today’s key exchange RSA‑2048

Ordinary computerLonger than the age of the universe

Large quantum computerUnder a week2

PacketLoq’s keys AES‑256

Ordinary computerFar longer than the age of the universe

Large quantum computer, with GroverHundreds of billions of times the age of the universe

Generous assumptions, in the attacker’s favor: Grover still needs about 2¹²⁸ steps, and spreading it across many machines helps far less than you’d hope. Even at a billion steps a second, that’s around 10²² years.3

Request a demonstration ← Back to the home page

↑