With the prevalence of outsourced computation, such as Machine Learning as a Service, protecting the privacy of sensitive data throughout the whole computation is a critical yet challenging task. The problem becomes even more tricky when multiple sources of input and/or multiple recipients of output are involved, who would encrypt/decrypt data using different keys. Considering many computation tasks demand binary operands and operations but there are only outsourced computation constructions for arithmetic calculations, in this paper, the authors propose a privacy-preserving outsourced computation framework for Boolean circuits. The proposed framework can protect sensitive data throughout the whole computation, i.e., input, output and all the intermediate values, ensuring privacy for general outsourced tasks. Moreover, it compresses the ciphertext domain of Liu et al., (2016) and attains secure protocols for four logic gates (AND, OR, NOT, and XOR) which are the basic operations in Boo