A checksum is a value that is computed from a data set. It's often used to check the integrity of data that's being transmitted or stored. If the computed checksum matches the provided checksum, it's assumed that the data hasn't been altered.
Hash validation checks that downloaded files haven't been altered by comparing their hash to a known good value.
In cybersecurity, integrity refers to the assurance that the data is trustworthy and accurate. It's one of the three main tenets of information security, along with confidentiality and availability.
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