Password-authenticated key agreement (PAKE) is a cryptographic protocol used to establish a shared secret between two parties, without relying on pre-shared secrets or certificates. PAKE is particularly useful in situations where users do not have access to public key infrastructure (PKI) or where the parties do not know each other in advance.

A key agreement protocol is a process by which two or more parties agree on a shared secret key to be used for future communication. The purpose of this key is to ensure confidentiality, integrity, and authenticity of messages exchanged between the parties.

A PAKE protocol combines a cryptographic hash function and a password to establish a shared secret between two parties. The protocol first derives a key from the password using a hash function, and then uses that key to derive additional keys. These keys can be used for encryption, integrity protection, or authentication.

One of the advantages of PAKE is that it does not rely on PKI, which makes it suitable for use in environments where PKI is not available. PAKE protocols are also resistant to offline dictionary attacks, where an attacker tries to guess the password by hashing a large number of potential passwords in advance.

There are several PAKE protocols in use today, including SRP, SPEKE, and SPAKE2. SRP (Secure Remote Password) is a popular PAKE protocol that has been in use since the 1990s. It is widely used in secure email, instant messaging, and virtual private networks.

PAKE is not without its limitations. One of the main drawbacks is the requirement for the password to be stored in a hashed form on both sides of the communication. This can be problematic if one of the parties is compromised, as the attacker can use the hashed password to mount a dictionary attack and guess the password.

Overall, PAKE is a useful tool for establishing secure communication between parties in situations where PKI is not available or feasible. It offers a more secure alternative to traditional password-based authentication mechanisms, which can be vulnerable to brute-force attacks. As with any cryptographic protocol, it is important to choose a well-vetted PAKE protocol and to implement it correctly to ensure its security.