Assurance of the source and integrity of a message against specified adversarial capabilities. Digital signatures permit public verification, whereas a message authentication code uses a shared secret; encryption alone need not authenticate.
A keyed function producing a tag that a holder of the shared secret can verify. Its message authentication security requires that valid tags for new messages cannot be forged under the allowed adversarial queries. Unlike a digital signature, verification is not inherently public and the verifier also knows a key capable of making tags.
Combine a secret randomly selected almost strongly universal hash family member with a fresh secret output mask. An observed message authentication code tag leaves the hash-selection key hidden, and the conditional hash bound controls substitution forgery probability. The message itself need not be encrypted. Mask reuse can reveal hash differences; repeated-use guarantees require fresh masks and an appropriate analysis of verification information. A one-use polynomial construction needs only two secret field elements, even for a much longer message.

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Message authentication is a process used to verify the integrity and authenticity of a message. It ensures that a message has not been altered in transit and confirms the identity of the sender. This is crucial in various communication systems to prevent unauthorized access, tampering, and impersonation. Key concepts in message authentication include: 1. **Integrity**: Ensuring the message has not been modified during transmission. If any part of the message is altered, the integrity check will fail.