Signature Properties

Cryptography · Axiom Academy

Essential properties that digital signatures must satisfy for cryptographic security The most fundamental property: valid signatures must verify successfully . If Alice signs a message with her private key, anyone should be able to verify the signature using her public key. For all key pairs (sk, pk) and all messages m, if signature s is generated correctly, then verification must succeed. Without correctness, the signature scheme would be useless - even legitimate signatures would fail to verify. The core security property: it should be computationally infeasible to create valid signatures without the private key . This ensures that only the key holder can produce authentic signatures. Even with access to the public key and many valid message-signature pairs, an adversary cannot forge a signature on a new message. Unforgeability is what makes digital signatures valuable for authentication and prevents impersonation attacks. Security against unforgeability is measured by the adversary's capabilities. Different attack models grant the attacker varying degrees of power. Attack Models (from weakest to strongest) Key-Only Attack: Adversary has only the public key Known-Message Attack: Adversary sees valid signatures on messages they didn't choose Chosen-Message Attack (CMA): Adversary can request signatures on messages of their choice

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