This article proposes a competitive-evolving-committee proactive secret sharing. Every participant in the system has the opportunity to become a member of the holding committee and have sufficient anonymity. During the life cycle of serving as the holding committee members, they only send one message in the protocol without excessive interaction, and achieve receiver strong anonymity with a capability-based encryption scheme different from most public-key encryption schemes, at present named RiddleEncryption, which is also proposed in this paper. In RiddleEncryption the sender does not need to pay attention to the specific identity of the receiver but focuses on what kind of capability the receiver should have. Nobody can determine this kind of capability at the beginning of the system establishment. This article aims at depositing a secret in a distributed manner (e.g., blockchain) without excessive trust and to emphasize more anonymity and capability. The scheme can be used in the dynamic groups, authentication management, rights abuse prevention, and so on.

We study the problems of outsourcing computation where a computational weak client outsources its computation task to a powerful server. Our work focuses on the research about outsourcing polynomial functions. Based on Zhang and Safavi-Naini's work, we construct a private outsourcing computation scheme for polynomial functions. Our scheme can keep privacy of the outsourced data and function. It is efficient in the sense of amortization and satisfies public verification. Compared with Zhang and Safavi-Naini's work, our construction uses a new efficient verify-method and makes the verification process public (any other clients can verify the correctness of the results returned by the server using the public key).