A key exchange scheme based on lattice

We construct a key exchange scheme with session key security and Alice's privacy, assuming the hardness of "small integer solution" (SIS) problem and "learning with errors" (LWE) problem, which have worst-case to average-case reductions from lattice problems. Our key exchange scheme is the first lattice-based key exchange scheme with provable security. Moreover, our scheme can be modified to be secure under impersonation attack by adding an authentication step; also, it can be modified to be more efficient using a new variant of LWE.