Physical Keys and Encryption Keys

A physical key, such as a house key, is a piece of metal with cuts of differing depths. Typically there may be around 6 cuts, with five different possible depths for each cut. This allows 5⁶ = 15,625 possible keys.

Encryption keys, such as AES keys, are a string of bits, often 128 bits, for a total of 2¹²⁸ possible keys.

How long would a physical key have to be to have the same level of security as an encryption key? We'd need to solve

5ⁿ = 2¹²⁸

which means

n = 128 / log₂5 = 55.12.

So we'd need a key with around 55 notches.

This only takes into account combinatorial possibilities, not the difficulty of attacking a physical key or a binary key. There are incomparably more possibilities for binary keys, but encryption attacks can be automated and carried out remotely (unless a computer is air gapped). A physical lock can only be attacked in person. It takes a lock picker orders of magnitude more time to try a key than a password cracking program. On the other hand, locks aren't picked by trying thousands of keys.

Related post: Measuring cryptographic strength in liters of boiling water

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