Hacking is a lot of things. The most common way doesn’t involve computers at all- just social engineering. But the more traditional type of hacking involves exploiting a software bug to gain access to a system. The details of the exploit will vary depending on the system in question, but they’ll usually lead to some advantage like privilege escalation or remote code execution. These can then be used to steal a payload of valuable information, like passwords, SSNs for identity theft, credit card numbers for regular theft, etc.
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