A new key pre-distribution scheme for wireless sensor networks (WSNs) is proposed, offering improved network resilience compared to existing schemes. The scheme uses multiple key spaces derived from Blom's method, allowing nodes to share keys probabilistically while maintaining network connectivity. The scheme ensures that if fewer than a threshold number of nodes are compromised, the probability of communication between other nodes being compromised is close to zero. This threshold property enhances security by making it costly for an adversary to gain significant advantage. The scheme requires each node to store a small number of keys, reducing memory usage while maintaining resilience. It also introduces a two-hop-neighbor key pre-distribution approach, improving resilience by allowing nodes two hops away from a sender to receive messages. The scheme is analyzed in terms of network resilience and overhead, showing it is more efficient than previous probabilistic key pre-distribution methods. The paper also introduces a formal framework for analyzing key pre-distribution schemes, emphasizing the importance of precise security definitions. The scheme is shown to be more secure than existing methods, with a higher threshold for node compromise before network security is compromised. The analysis includes simulations and theoretical bounds, demonstrating the scheme's effectiveness in resisting node capture attacks.A new key pre-distribution scheme for wireless sensor networks (WSNs) is proposed, offering improved network resilience compared to existing schemes. The scheme uses multiple key spaces derived from Blom's method, allowing nodes to share keys probabilistically while maintaining network connectivity. The scheme ensures that if fewer than a threshold number of nodes are compromised, the probability of communication between other nodes being compromised is close to zero. This threshold property enhances security by making it costly for an adversary to gain significant advantage. The scheme requires each node to store a small number of keys, reducing memory usage while maintaining resilience. It also introduces a two-hop-neighbor key pre-distribution approach, improving resilience by allowing nodes two hops away from a sender to receive messages. The scheme is analyzed in terms of network resilience and overhead, showing it is more efficient than previous probabilistic key pre-distribution methods. The paper also introduces a formal framework for analyzing key pre-distribution schemes, emphasizing the importance of precise security definitions. The scheme is shown to be more secure than existing methods, with a higher threshold for node compromise before network security is compromised. The analysis includes simulations and theoretical bounds, demonstrating the scheme's effectiveness in resisting node capture attacks.