How does a simple checksum work, and what is its fundamental limitation?

Question

Accepted Answer

A checksum is a value derived from data to detect changes — but a simple one can miss errors that cancel out.
Example — use the digit sum (Quersumme) as a checksum:

Number 34567 → 3+4+5+6+7 = 25
Change one digit → the sum changes → error detected ✓
Change two digits that offset each other → the sum can stay the same → error missed ✗

Real-world simple checksums work the same way: ISBN, credit-card numbers (Luhn), CRC-16/32. The ISBN-13 check digit, for instance, weights digits ×1,×3,×1,×3… sums them, and picks the digit that rounds up to the next multiple of 10.
Why it matters: simple checksums catch accidental single-point errors but give no protection against a deliberate attacker, who can craft changes that preserve the checksum. For that you need cryptographic hashes or signatures.
Tip: Checksum = error detection, not security. If an attacker can recompute it, it protects nothing.