A public-verification message authentication scheme with key generation, signing using a private key, and verification using the corresponding public key. Signing an appropriate digest binds the signature to the message; encryption alone does not provide this authenticity.
A digital signature attack with a signing oracle for adversary-selected messages. A forgery must authenticate a message not previously submitted to that oracle.
A digital signature attack using legitimate message–signature pairs whose messages were not selected by the adversary.
A digital signature attack using the public scheme and verification public key, without supplied signed-message examples or a signing oracle.
The ability to produce a valid digital signature for an arbitrary specified target message. Under a chosen-message signature attack, the target must not have been submitted to the signing oracle.
Producing a valid digital signature on some new message under the specified attack model, without necessarily controlling that message's content in advance.
For a prime number , primitive root and public key , choose a fresh secret coprime to , set and , and verify . Reusing the cryptographic nonce can reveal secret information. The unhashed historical construction allows existential forgery of specially chosen message exponents, so authentication claims require suitable hashing and protocol assumptions.
A signature based on private RSA cryptosystem exponentiation, with public exponentiation used for verification. Textbook is multiplicatively forgeable; a secure scheme requires an appropriate encoding and message digest rather than raw message exponentiation.

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A digital signature is a cryptographic mechanism that provides a means to verify the authenticity and integrity of digital messages or documents. It serves a function similar to a handwritten signature or a stamped seal but offers far more inherent security. ### Key Features of Digital Signatures 1. **Authentication**: Digital signatures help confirm the identity of the individual or entity that has signed the document, ensuring that the recipient knows who the sender is.