Quantum-safe forward secure password authenticated key life-cycle management scheme with key update mechanism

In this paper we construct and consider a new password authenticated key life-cycle management scheme (PAKMS) with key update mechanism, which uses random q-ary lattices as its domain. We justify that the scheme is existentially forward unforgeable under a chosen password attack (fu-cpwda). To this end, we show that breaking this scheme let us to construct a polynomial-time adversary that is able to solve small integer solution (SIS) problem. Since the security of the scheme is based on computational hardness of SIS problem, it tuns out to be resistant to both classical and quantum computations. The keyupdating mechanism is based on some properties of binary trees, with a number of leaves being the same as a number of time periods in the scheme. The forward-security is gained under the assumption that one out of two hash functions is modeled as a random oracle.