Authentication is a two-party cryptographic functionality that enables one party (the verifier) to confirm the identity of another party (the prover), or to verify the authenticity of a message claimed to originate from a particular party. It serves as the foundational layer for secure access control, communication, and trust establishment in both classical and quantum settings.

There are two primary branches of this functionality:

• Identification (Identity Authentication): Verifies who is communicating. That is, the prover proves their identity to the verifier, typically using secret credentials or cryptographic keys. This is often used for login, access control, and user verification.
• Message Authentication: Verifies that a specific message was sent by a particular sender and has not been altered. This is typically achieved using message authentication codes (MACs) or digital signatures.

These two variants are often used instead of each other, but conceptually and technically, they are distinct cryptographic functionalities.
Authentication can be achieved both in the symmetric-key settings, via challenge-response protocols, or in the asymmetric setting through public-key schemes.

Authentication is a fundamental classical functionality, both message and entity authentication can be achieved in the classical setting:

Message Authentication has well-established classical implementations:

• MACs using shared symmetric keys (e.g., HMAC-SHA256).
• Digital Signatures using public-key infrastructure (e.g., RSA, ECDSA).

Identity Authentication:

• Password-based login protocols.
• Zero-knowledge identification protocols (e.g., Fiat-Shamir protocol).
• Public-key challenge-response authentication.

Authentication has a myriad of real-world use cases in almost any standard secure schemes used in the web, banking, login systems, emails and so on. Digital signatures are also used for legal and financial documents. It is also crucial in Blockchain and smart contracts, ensuring message provenance.

The main security property of authentication schemes is unforgeability.
Unforgeability: It ensures adversaries cannot produce valid messages or responses without the appropriate credentials, and hence cannot fake the identity of another party or a message.

There are other properties such as:

• Integrity: Guarantees that a message has not been tampered with.
• Replay Protection: Protocols can include timestamps to prevent reuse of valid responses.

Quantum-Secure Authentication: In the quantum world, authentication schemes should also provide security against quantum adversaries.

• Quantum-secure signatures can be made based on assumptions like LWE, hash-based signatures (e.g., SPHINCS+), or code-based cryptography.
• Quantum-secure MACS: There exists a quantum-secure version of Wegman-Carter MAC.
• Quantum-secure authentication and identification protocols can also be constructed using hardware assumptions and quantum communication

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