The invention relates to an identity authentication and key negotiation method. In order to overcome the defects in the prior art that security of authentication methods is not high, the invention discloses an identity authentication and shared key generation method. In the technical solution of the invention, a key authority issues a pair of public key and private key which are matched, and sets a correlation coefficient k, an offset vector {right arrow over (e)}, a regression coefficient a, a modulus m as well as , and {right arrow over (e)}. Further, if a device i and a device j are any two devices, the matched public key and private key thereof satisfy the condition k×({right arrow over (pi)}×{right arrow over (sjT)}+{right arrow over (pi)}×{right arrow over (eT+)}a)≡k×({right arrow over (pj)}×{right arrow over (siT)}+{right arrow over (pj)}×{right arrow over (eT)}+a)mod m; wherein the {right arrow over (siT)} is a transposed vector of the {right arrow over (si)}, the {right arrow over (eT)} is a transposed vector of the {right arrow over (e)}, and the {right arrow over (sjT)} is a transposed vector of the {right arrow over (sj)}. Provided that a device A is an authentication initiator, a matched public key thereof is {right arrow over (pA)} and a matched private key thereof is {right arrow over (sA)}; and a device B is an authentication participant, a matched public key thereof is {right arrow over (pB)} and a matched private key thereof is {right arrow over (sB)}. The authentication between the device A and the device B succeeds under the following condition: k×({right arrow over (pA)}×{right arrow over (sBT)}+{right arrow over (pA)}×{right arrow over (eT+)}a)≡k×({right arrow over (pB)}×{right arrow over (sAT)}+{right arrow over (pB)}×{right arrow over (eT+)}a)mod m. The invention is particularly applicable to chips.