Digital signatures provide integrity, authenticity, and typically non-repudiation by using an asymmetric key pair. The signer uses the private key to create a signature over a message (usually over a hash/digest of the message). Because the private key is kept secret, only the legitimate signer should be able to produce a valid signature. Anyone who has the corresponding public key can then validate the signature: they verify that the signature matches the message digest under the public key and that the signed data has not been altered. This is why the public key can be widely distributed (often inside an X.509 certificate) while the private key must be protected by the signer. If a public key were used to sign, anyone could forge signatures; if a private key were required for validation, only the signer could validate, defeating the purpose of public verifiability. Therefore, the correct key roles are private key for signing and public key for signature validation.
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