Improvement and applications of secure outsourcing of scientific computations

Methods for solving equations play an important role in scientific computation and cryptography. Usually, many cryptographic protocols and scientific computation problems can be reduced to some differential equation or linear equation systems. However, the above mentioned scientific computation needs very much computation resource. Hence, super computer technology such as grid technology, cloud computation is slow to emerge. Cloud computation has strong computation power and helps users to deals with this very difficult computation. For security, we need improve some conditional computation methods for numerical or scientific outsourcing computation. In this paper some special algebraic and differential equations are studied. And some new practical verifiably secure outsourcing protocols are designed, which are better than the previous methods in the following terms. First, they can protect more secret parameters for abstract equations. Second, based on previous methods, random function can be chosen in the different ways and hence better security and privacy is obtained. Third, for nonlinear equations, we find more applications and new methods. These tools help us to find more methods to deal with more linear or nonlinear equations. At last, some verifiably secure outsourcing computation for integral computation is designed. These results help to outsource the computation for solving differential equations.