In the realm of software security, a core concept lies in the "attack surface." Envision a house with numerous doors and windows left ajar, inviting more opportunities for thieves. Similarly, an attack surface in a software context refers to all avenues through which hackers can gain unauthorized access or extract data. The magnitude of a system's attack surface is a direct reflection of its overall security posture.

If a system resembles a castle with myriad entry and exit points, the threats it confronts are naturally heightened. Hence, minimizing the attack surface—akin to securing unnecessary openings—forms the bedrock of ensuring software safety.

How do these hackers leverage the attack surface for infiltration? Their "keys" are attack vectors such as buffer overflows, network protocol vulnerabilities, or Trojan horses, adware, malware embedded within web pages. Identifying a single weakness in the system, like an unlocked window, provides an opening for exploitation.

It's crucial to note that even a significantly reduced attack surface doesn't entirely prevent post-intrusion damage. Once hackers breach defenses, the aftermath can still be severe; leaving just one door unlocked can still lead to a complete ransacking.

During an intrusion, hackers first conduct comprehensive reconnaissance of the target system, mapping out devices and connections akin to charting a treasure map. They then seek and exploit potential vulnerabilities at every node.

To build impervious systems, we must strive to shrink the attack surface. This necessitates fundamental security measures:

- Streamline code: The less code running, the fewer vulnerabilities exist for exploitation. It's akin to removing extraneous furniture from a room to eliminate hiding spots.

- Restrict system entry points: Fewer entry points limit the paths for hackers to attempt breaches, similar to installing fewer but sturdier doors in a house.

- Disable seldom-used services: Just as sealing off an infrequently used room reduces invasion risks, turning off unnecessary functions strengthens the security perimeter.

In summary, maintaining software security parallels safeguarding one's home, requiring constant vigilance and reinforcement to deny attackers any opportunity. In this digital era, every minor security measure serves as a vital shield for our digital assets.