Today, the Internet trust is a critical framework that forms a fundamental premise for network security. Several identity federations are deployed to embody the classic theory of trust framework. However, in an emerging blockchain-based decentralized system, we need to model dynamically grown/shrunken trust. This paper models the trust elasticity by formalizing PDP(policy decision point)s of enrolling entities and introducing Trust PDP. In the proposed formalization, assertions are exchanged among participating nodes to express the knowledge of the PDP of nodes. The knowledge may grow by exchanging assertions. Furthermore, we propose exchanging assertions on the trust relationship to express the elasticity of trust. The judgment on trust is operated by Trust PDP that affects the elasticity of trust. The proposed theory is applied to the trust establishment of blockchain and an authorization management system based on blockchain. The trust in the blockchain environment is expressed in terms of Trust PDP.