Consider a scenario where an attacker attempts to generate private keys at random and calculates the corresponding public keys, aiming to match them with a known set of 100 public addresses. Assuming a cryptographic system like Bitcoin that employs the Elliptic Curve Digital Signature Algorithm (ECDSA) for key generation:
- What is the probability of randomly generating a single correct private key corresponding to one specific public address?
- Given a set of 100 specific public addresses, what is the probability of successfully matching at least one of these addresses with a randomly generated private key?
- How does the size of the key space (2^256 for ECDSA) influence the feasibility of such brute-force attacks?
- Are there any practical limitations or considerations that further reduce the probability of success beyond theoretical calculations?
In essence, this question aims to explore the theoretical and practical limitations of brute-forcing private keys to match specific public addresses in a cryptocurrency system, considering the vastness of the key space and cryptographic security measures.