アクセス制御状態の4分類

The security of individual keys was widely studied with practical solutions available, from mnemonic phrases to dedicated hardware. There are also techniques for securing funds by requiring combinations of multiple keys. However, to the best of our knowledge, a crucial question was never addressed: How is wallet security affected by the number of keys, their types, and how they are combined? This is the focus of this work.

We present a model where each key has certain probabilities for being safe, lost, leaked, or stolen (available only to an attacker). The number of possible wallets for a given number of keys is the Dedekind number, prohibiting an exhaustive search with many keys. Nonetheless, we bound optimal-wallet failure probabilities with an evolutionary algorithm.

safe	Only the user has access,
loss	No one has access,
leak	Both the user and the adversary have access, or
theft	Only the adversary has access

Once you know these states, you can assign probabilities of transitioning from one state to another (someone hacks your account and locks you out, you forgot your own password, etc.) and then build optimal security and reliability to deal with it.