self doubt

Question

why  a single secret key cannot be used by the sender to sign multiple documents for multiple receiver.

please explain

Comments

what i think is bcoz any receivers may confuse for which packets to recieve since all docs have same  digital sign.

if different secret keys are used to sign then each reciever is  confined  to  receive uniquely signed packets.

Am I correct or not?

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It depends on the purpose of signature.

DS is used for Authentication, integrity, non-repudiation.

Private key is selected from the set of possible private keys produced in RSA. RSA always generates unique pair of public private key pair. The receiver should have the same public key which can decrypt the document signed using private key in that pair. If security required is more, you can generate different keys but at the cost of computational costs + key management. If you just want to avoid intruders reading/modifying and provide authentication, single secret key is okay.