Recall from our previous post that the main security statement of Subspace consensus is the following:
“Given some honest storage \Omega, an always-online adversary must control or fake a storage of at least \Omega/\phi_c (1 + \lambda \Delta) in order to break the security (with high probability).”
This is an asymptotic result, meaning that the adversary can break the security with high probability no matter what the confirmation depth is. In practice, we may be interested in the following, non-asymptotic, question: Given certain fraction of adversary storage (owned or faked) and confirmation depth k, what is the probability that the adversary can break the security (by conducting a double-spending attack on a target transaction)? Intuitively, such probability should decrease with k.
Saeid (our research assistant) will help us understand such probability for two special cases (c \to \infty and c = 1), since these two cases can be reduced to some known results in the literature called settlement bounds.
Correction: Only one special case (c \to \infty) is discussed in the literature. To the best of my knowledge, the settlements bounds for c = 1 is still open.