In a method for efficient password based public key authentication between a first user device and a second user device, a shared password is received by a first user device which generates a first hash value of the shared password and a first value, wherein the first value is composed of at least a product of the first hash value and a first unique security constant associated with the first user. The first user device then generates a first random value generated using data from a generator element, and a first blind public key associated with the first user device, wherein the first blind public key is generated using a first public key. The first user device concurrently sends the first value and the first blind public key to the second user device for authentication.