Big data has a strong demand for a network infrastructure with the capability to support data sharing and retrieval efficiently. Information-centric networking (ICN) is an emerging approach to satisfy this demand, where big data is cached ubiquitously in the network and retrieved using data names. However, existing authentication and authorization schemes rely mostly on centralized servers to provide certification and mediation services for data retrieval. This causes considerable traffic overhead for the secure distributed sharing of data. To solve this problem, we employ identity-based cryptography (IBC) to propose a Distributed Authentication and Authorization Scheme (DAAS), where an identity-based signature (IBS) is used to achieve distributed verifications of the identities of publishers and users. Moreover, Ciphertext-Policy Attribute-based encryption (CP-ABE) is used to enable the distributed and fine-grained authorization. DAAS consists of three phases: initialization, secure data publication, and secure data retrieval, which seamlessly integrate authentication and authorization with the interest/data communication paradigm in ICN. In particular, we propose trustworthy registration and Network Operator and Authority Manifest (NOAM) dissemination to provide initial secure registration and enable efficient authentication for global data retrieval. Meanwhile, Attribute Manifest (AM) distribution coupled with automatic attribute update is proposed to reduce the cost of attribute retrieval. We examine the performance of the proposed DAAS, which shows that it can achieve a lower bandwidth cost than existing schemes.