A security authentication method applied to wireless fidelity Wi-Fi, comprising: negotiating, by an access point AP based on a password, a pairwise master key PMK with a first device based on a twin base password encrypted key exchange TBPEKE protocol, wherein the password is a shared key between the AP and the first device; and performing, by the AP, a 4-way handshake with the first device based on the PMK; wherein the PMK comprises a first PMK1 and a second PMK2, and the negotiating, by an access point AP based on a password, a pairwise master key PMK with a first device based on a twin base password encrypted key exchange TBPEKE protocol comprises: obtaining, by the AP, a first parameter X from the first device, wherein the first parameter X is determined based on a hash-to-curve function g, the hash-to-curve function g is for converting the password into a point on an elliptic curve through a point multiplication operation, X=g x, and x is a random number; sending, by the AP, a second parameter Y to the first device, to indicate the first device to calculate the first PMK1 based on the first parameter X and the second parameter Y, wherein the second parameter Y is determined based on the hash-to-curve function g, Y=g y, and y is a random number; and calculating, by the AP, the second PMK2 based on the first parameter X and the second parameter Y; wherein the hash-to-curve function g is represented as: g=U·V pw, wherein U and V are two independent random generating elements obtained from a cyclic group G whose order is a prime p, and pw represents the password; and wherein the hash-to-curve function g is pre-stored locally in the AP, and the password pw is not pre-stored locally in the AP. negotiating, by an access point AP based on a password, a pairwise master key PMK with a first device based on a twin base password encrypted key exchange TBPEKE protocol, wherein the password is a shared key between the AP and the first device; and performing, by the AP, a 4-way handshake with the first device based on the PMK; wherein the PMK comprises a first PMK1 and a second PMK2, and the negotiating, by an access point AP based on a password, a pairwise master key PMK with a first device based on a twin base password encrypted key exchange TBPEKE protocol comprises: obtaining, by the AP, a first parameter X from the first device, wherein the first parameter X is determined based on a hash-to-curve function g, the hash-to-curve function g is for converting the password into a point on an elliptic curve through a point multiplication operation, X=g x, and x is a random number; sending, by the AP, a second parameter Y to the first device, to indicate the first device to calculate the first PMK1 based on the first parameter X and the second parameter Y, wherein the second parameter Y is determined based on the hash-to-curve function g, Y=g y, and y is a random number; and calculating, by the AP, the second PMK2 based on the first parameter X and the second parameter Y; wherein the hash-to-curve function g is represented as: g=U·V pw, wherein U and V are two independent random generating elements obtained from a cyclic group G whose order is a prime p, and pw represents the password; and wherein the hash-to-curve function g is pre-stored locally in the AP, and the password pw is not pre-stored locally in the AP. obtaining, by the AP, a first parameter X from the first device, wherein the first parameter X is determined based on a hash-to-curve function g, the hash-to-curve function g is for converting the password into a point on an elliptic curve through a point multiplication operation, X=g x, and x is a random number; sending, by the AP, a second parameter Y to the first device, to indicate the first device to calculate the first PMK1 based on the first parameter X and the second parameter Y, wherein the second parameter Y is determined based on the hash-to-curve function g, Y=g y, and y is a random number; and calculating, by the AP, the second PMK2 based on the first parameter X and the second parameter Y; wherein the hash-to-curve function g is represented as: g=U·V pw, wherein U and V are two independent random generating elements obtained from a cyclic group G whose order is a prime p, and pw represents the password; and wherein the hash-to-curve function g is pre-stored locally in the AP, and the password pw is not pre-stored locally in the AP.