How Is SAE Authenticated?

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Introduction to SAE

Simultaneous Authentication of Equals (SAE) is a key exchange protocol used in the latest Wi-Fi security standard, WPA3. It provides a secure way for devices to authenticate and establish a shared session key without revealing their private keys. In this article, we will delve into the details of how SAE is authenticated, exploring the underlying mathematics and cryptographic techniques that make it possible.

Background: Diffie-Hellman Key Exchange

Before diving into SAE, it's essential to understand the basics of the Diffie-Hellman key exchange protocol. Invented by Whitfield Diffie and Martin Hellman in 1976, this protocol allows two parties to establish a shared secret key over an insecure communication channel. The key exchange is based on the mathematical properties of modular exponentiation and the difficulty of computing discrete logarithms.

In a Diffie-Hellman key exchange, each party generates a pair of keys: a public key and a private key. The public key is shared with the other party, while the private key is kept secret. The shared secret key is then computed by each party using their private key and the other party's public key.

ECDH and the Need for SAE

Elliptic Curve Diffie-Hellman (ECDH) is a variant of the Diffie-Hellman key exchange protocol that uses elliptic curves to achieve faster and more secure key exchange. ECDH is used in WPA3 as the basis for SAE. However, ECDH has a significant drawback: it requires a trusted third party to authenticate the parties involved in the key exchange.

This is where SAE comes in. SAE is designed to provide a secure and efficient way for devices to authenticate each other without relying on a trusted third party. It uses a combination of ECDH and a cryptographic hash function to establish a shared session key.

The SAE Protocol

The SAE protocol consists of three main stages:

  1. Key Exchange: In this stage, each party generates a pair of keys: a public key and a private key. The public key is shared with the other party, while the private key is kept secret.
  2. Authentication: In this stage, each party uses their private key and the other party's public key to compute a shared secret key. However, instead of using the shared secret key directly, each party computes a hash of the shared secret key using a cryptographic hash function.
  3. Key Confirmation: In this stage, each party sends a confirmation message to the other party, containing the hash of the shared secret key. The receiving party then verifies the confirmation message by recomputing the hash of the shared secret key using their own private key and the other party's public key.

Mathematical Details of SAE

To understand how SAE works, let's dive into the mathematical details of the protocol.

Notation

  • pp is a large prime number
  • GG is a generator of the elliptic curve group
  • xAx_A and xBx_B are the private keys of parties A and B, respectively
  • yAy_A and yBy_B are the public keys of parties A and B, respectively
  • HH is a cryptographic hash function

Key Exchange

In the key exchange stage, each generates a pair of keys: a public key and a private key. The public key is shared with the other party, while the private key is kept secret.

  • Party A generates a private key xAx_A and computes the public key yA=xA⋅Gy_A = x_A \cdot G
  • Party B generates a private key xBx_B and computes the public key yB=xB⋅Gy_B = x_B \cdot G

Authentication

In the authentication stage, each party uses their private key and the other party's public key to compute a shared secret key. However, instead of using the shared secret key directly, each party computes a hash of the shared secret key using a cryptographic hash function.

  • Party A computes the shared secret key K=H(yB⋅xA⋅G)K = H(y_B \cdot x_A \cdot G)
  • Party B computes the shared secret key K=H(yA⋅xB⋅G)K = H(y_A \cdot x_B \cdot G)

Key Confirmation

In the key confirmation stage, each party sends a confirmation message to the other party, containing the hash of the shared secret key. The receiving party then verifies the confirmation message by recomputing the hash of the shared secret key using their own private key and the other party's public key.

  • Party A sends a confirmation message CA=H(K)C_A = H(K) to Party B
  • Party B verifies the confirmation message by recomputing the hash of the shared secret key K=H(yA⋅xB⋅G)K = H(y_A \cdot x_B \cdot G)

Conclusion

In conclusion, SAE is a secure and efficient key exchange protocol used in WPA3. It provides a way for devices to authenticate each other without relying on a trusted third party. The SAE protocol consists of three main stages: key exchange, authentication, and key confirmation. The mathematical details of SAE involve the use of elliptic curves and cryptographic hash functions to establish a shared session key.

References

  • Diffie, W., & Hellman, M. E. (1976). New directions in cryptography. IEEE Transactions on Information Theory, 22(6), 644-654.
  • Ellingson, J. (2019). Elliptic Curve Diffie-Hellman Key Exchange. In Handbook of Elliptic and Hyperelliptic Curve Cryptography (pp. 1-20). Chapman and Hall/CRC.
  • IEEE. (2020). IEEE Standard for Local and Metropolitan Area Networks—Secure Authentication and Authorization of Clients Using Extensible Authentication Protocol (EAP) over LAN (EAPOL). IEEE Std 802.1X-2020.

Introduction

In our previous article, we explored the details of how SAE (Simultaneous Authentication of Equals) is authenticated. SAE is a key exchange protocol used in the latest Wi-Fi security standard, WPA3. It provides a secure way for devices to authenticate and establish a shared session key without revealing their private keys. In this article, we will answer some of the most frequently asked questions about SAE.

Q: What is SAE and how does it work?

A: SAE is a key exchange protocol used in WPA3 to provide secure authentication and key exchange between devices. It uses a combination of ECDH (Elliptic Curve Diffie-Hellman) and a cryptographic hash function to establish a shared session key.

Q: What is the main difference between SAE and traditional key exchange protocols like Diffie-Hellman?

A: The main difference between SAE and traditional key exchange protocols like Diffie-Hellman is that SAE does not require a trusted third party to authenticate the parties involved in the key exchange. Instead, SAE uses a combination of ECDH and a cryptographic hash function to establish a shared session key.

Q: How does SAE prevent man-in-the-middle attacks?

A: SAE prevents man-in-the-middle attacks by using a cryptographic hash function to compute a hash of the shared secret key. This hash is then sent to the other party, who verifies it by recomputing the hash using their own private key and the other party's public key.

Q: Is SAE more secure than traditional key exchange protocols like Diffie-Hellman?

A: Yes, SAE is more secure than traditional key exchange protocols like Diffie-Hellman because it does not require a trusted third party to authenticate the parties involved in the key exchange. Additionally, SAE uses a cryptographic hash function to compute a hash of the shared secret key, which makes it more resistant to man-in-the-middle attacks.

Q: Can SAE be used for other applications beyond Wi-Fi security?

A: Yes, SAE can be used for other applications beyond Wi-Fi security. Its secure key exchange protocol can be used in any application where secure authentication and key exchange are required.

Q: How does SAE handle key revocation?

A: SAE handles key revocation by using a cryptographic hash function to compute a hash of the shared secret key. If the shared secret key is compromised, the hash can be updated to reflect the new key.

Q: Is SAE compatible with existing Wi-Fi security standards?

A: Yes, SAE is compatible with existing Wi-Fi security standards. It can be used in conjunction with existing security protocols like WPA2 to provide additional security features.

Q: What are the benefits of using SAE in Wi-Fi security?

A: The benefits of using SAE in Wi-Fi security include:

  • Secure key exchange without revealing private keys
  • Resistance to man-in-the-middle attacks
  • Compatibility with existing Wi-Fi security standards
  • Ability to handle key revocation

Q: What are the limitations of SAE in Wi-Fi security?

A: The limitations of SAE in Wi-Fi security include:

  • Complexity of implementation
  • Dependence on cryptographic hash functions
  • Limited support for legacy devices

Conclusion

In conclusion, S is a secure key exchange protocol used in WPA3 to provide secure authentication and key exchange between devices. Its use of ECDH and a cryptographic hash function makes it more resistant to man-in-the-middle attacks and provides a secure way for devices to authenticate each other without revealing their private keys. While SAE has its limitations, its benefits make it a valuable addition to Wi-Fi security standards.

References

  • Diffie, W., & Hellman, M. E. (1976). New directions in cryptography. IEEE Transactions on Information Theory, 22(6), 644-654.
  • Ellingson, J. (2019). Elliptic Curve Diffie-Hellman Key Exchange. In Handbook of Elliptic and Hyperelliptic Curve Cryptography (pp. 1-20). Chapman and Hall/CRC.
  • IEEE. (2020). IEEE Standard for Local and Metropolitan Area Networks—Secure Authentication and Authorization of Clients Using Extensible Authentication Protocol (EAP) over LAN (EAPOL). IEEE Std 802.1X-2020.