Cryptanalysis of LWE and SIS-based cryptosystems by using quantum annealing

In the paper, we study lattice-based cryptographic problems, in particular Learning With Errors (LWE) and Short Integer Solution (SIS) lattice problems, which are considered to be known cryptographic primitives that are supposed to be secure against both classical and quantum attacks. We formulated the LWE and SIS problems as Mixed-Integer Programming (MIP) model and then converted them to Quadratic Unconstrained Binary Optimization (QUBO) problem, which can be solved by using a quantum annealer. Quantum annealing searches for the global minimum of an input objective function subjected to the given constraints to optimize the given model. We have estimated the q-bits required for the Quantum Processing Unit (QPU). Our results show that this approach can solve certain instances of the LWE and SIS problems efficiently.