Common use of Brute Force Attack on the Master Keys Clause in Contracts

Brute Force Attack on the Master Keys. Similarly, to solve for all of the master keys using the captured private keys without knowing the PPMka information, the number of possible sets of m × m linear equations is also given in Equation (12). Each attempt involves constructing the (m × m) system of linear equations, solving them using, say, the Gaussian elimination method and testing each solution to see if it can successfully compute a captured node’s private key using one of its public keys. The possible number of solutions is also given in Table 2. Hence, due to the unknown PPMka in the BYka scheme, there is only a probabilistic chance of breaking the scheme, even if sufficient captured keys are available. With suitable keying parameters, the chance can be made so small, that the scheme cannot be feasibly broken. However, the scheme can be broken if the PPMka can be discovered. We show next how discovering the PPMka can be made very difficult by using key operations over a small prime field Fp.