📐Mathematical Modeling

The security of multi-signature setups and secure element chips can be modeled mathematically to ensure robustness:

Multi-Signature Security Model

The security of a multi-signature system can be expressed as:

$$P(\text{Transaction}) = \prod_{i=1}^{n} P(\text{Signature}_i)$$

Where:

P(Signature_i) represents the probability that each individual keyholder signs the transaction.

For a transaction to be executed, all required signatures must be provided, reducing the risk of unauthorized transactions.

Secure Element Tamper Resistance

The probability of a successful attack on the secure element can be modeled as:

$$P(\text{Attack Success}) = 1 - \prod_{i=1}^{m} P(\text{Failure}_i)$$

Where:

P(Failure_i) represents the probability that each tamper-resistance mechanism within the secure element will resist an attack.