A scheme that can realize homomorphic Turing- equivalent privacy-preserving computations is proposed, where the encoding of the Turing machine is independent of its inputs and running time. Several extended private in...A scheme that can realize homomorphic Turing- equivalent privacy-preserving computations is proposed, where the encoding of the Turing machine is independent of its inputs and running time. Several extended private information retrieval protocols based on fully homomorphic encryption are designed, so that the reading and writing of the tape of the Turing machine, as well as the evaluation of the transition function of the Turing machine, can be performed by the permitted Boolean circuits of fully homomorphic encryption schemes. This scheme overwhelms the Turing-machine-to- circuit conversion approach, which also implements the Turing-equivalent computation. The encoding of a Turing- machine-to-circuit conversion approach is dependent on both the input data and the worst-case runtime. The proposed scheme efficiently provides the confidentiality of both program and data of the delegator in the delegator-worker model of outsourced computation against semi-honest workers.展开更多
This paper starts from the analysis of how Alan Turing proceeded to build the notion of computability in his famous 1936 text ＂On computable numbers, with an application to the Entscheidungsproblem＂. Looking in deta...This paper starts from the analysis of how Alan Turing proceeded to build the notion of computability in his famous 1936 text ＂On computable numbers, with an application to the Entscheidungsproblem＂. Looking in detail at his stepwise construction, which starts from the materialities to achieve a satisfactory level of abstraction, it is considered how his way of doing mathematics was one that constructs mathematical knowledge by evading a definite separation between matter and form; in this way, making the world and language come together. Following the same line of reasoning, it is argued in this paper that the abstract and the concrete, the deduction and the induction, the technical and the social as well as the objective and the subjective are unthinkable as pure entities. By considering the controversies and discussions from the mid-nineteenth century until now, it is shown that local （social） elements necessarily participate in what is usually considered ＂technical content＂ or ＂objectivity＂. While Alan Turing was a precursor of what today might be said to be an ＂anthropological approach to mathematical culture＂, unveiling and reviving approaches that enable the axis of authority for mathematics, logic and computing to be shifted, he also opened different paths for the construction of a variety of mathematical knowledge as well.展开更多
基金The National Basic Research Program of China(973Program)(No.2013CB338003)
文摘A scheme that can realize homomorphic Turing- equivalent privacy-preserving computations is proposed, where the encoding of the Turing machine is independent of its inputs and running time. Several extended private information retrieval protocols based on fully homomorphic encryption are designed, so that the reading and writing of the tape of the Turing machine, as well as the evaluation of the transition function of the Turing machine, can be performed by the permitted Boolean circuits of fully homomorphic encryption schemes. This scheme overwhelms the Turing-machine-to- circuit conversion approach, which also implements the Turing-equivalent computation. The encoding of a Turing- machine-to-circuit conversion approach is dependent on both the input data and the worst-case runtime. The proposed scheme efficiently provides the confidentiality of both program and data of the delegator in the delegator-worker model of outsourced computation against semi-honest workers.
文摘This paper starts from the analysis of how Alan Turing proceeded to build the notion of computability in his famous 1936 text ＂On computable numbers, with an application to the Entscheidungsproblem＂. Looking in detail at his stepwise construction, which starts from the materialities to achieve a satisfactory level of abstraction, it is considered how his way of doing mathematics was one that constructs mathematical knowledge by evading a definite separation between matter and form; in this way, making the world and language come together. Following the same line of reasoning, it is argued in this paper that the abstract and the concrete, the deduction and the induction, the technical and the social as well as the objective and the subjective are unthinkable as pure entities. By considering the controversies and discussions from the mid-nineteenth century until now, it is shown that local （social） elements necessarily participate in what is usually considered ＂technical content＂ or ＂objectivity＂. While Alan Turing was a precursor of what today might be said to be an ＂anthropological approach to mathematical culture＂, unveiling and reviving approaches that enable the axis of authority for mathematics, logic and computing to be shifted, he also opened different paths for the construction of a variety of mathematical knowledge as well.
