A checksum and a digital signature aren’t the same thing. If you have a data block and a checksum of the data block, the data block can be modified and a new checksum can be computed to reflect the modifications. Instead of a checksum would be a digital signature using an asymmetric key. The data block would be modified but the signature of that block can’t be recomputed without the key used to sign it, which is not part of the transfer.
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