Trust brings a new method for building scalable and fine-grained access control mechanism in P2P systems. The quantificational expression of trust and the calculation of trust in a trust network are the basis of trust degree based access control. In this paper, the properties of trust is analyzed by referring to the fruits from social science; the semantics of trust in the context of access control is described, and a trust degree based access control model named TDBAC is introduced. Basing on the properties and semantics of trust, a computational trust model which includes a multilevel comprehensive evaluation method for expressing direct trust and calculators for computing recommended trust is put forward. To compute trust in a trust network, an algorithm that transforms a trust network to a computable expression is given. The algorithm simplifies the computation process and is also flexible. Trust brings a new method for building scalable and fine-grained access control mechanism in P2P systems. The quantificational expression of trust and the calculation of trust in a trust network are the basis of trust degree based access control. In this paper, the properties of trust is analyzed by referring to the fruits from social science; the semantics of trust in the context of access control is described, and a trust degree based access control model named TDBAC is introduced. Basing on the properties and semantics of trust, a computational trust model which includes a multilevel comprehensive evaluation method for expressing direct trust and calculators for computing recommended trust is put forward. To compute trust in a trust network, an algorithm that transforms a trust network to a computable expression is given. and is also flexible