Provable Security is a formal method for proving the security of cryptographic schemes, in which the difficulty of breaking a particular scheme is formally related to that of solving a widely believed computational hard problem. Provable security has already become an important theme of theoretical researches in modern cryptography. This dissertation investigates the provable security of public-key encryptions and hybrid encryptions of asymmetric and symmetric encryptions. This includes the various formal security notions and the constructions can be proved to achieve them. Among the constructions, hybrid encryptions are themselves an important way to obtain public-key encryption schemes with chosen ciphertext security. The main results are as follows:(1) The one-wayness of the trapdoor one-way function in NTRU depends on the randomness of the session key, which is different from previous ones. Based on this observation, a new kind of trapdoor one-way function, trapdoor one-way functions with an auxiliary random variable is proposed.

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The numerical calculation of grounding grid in large-scale substation under different conditions are carried out, including the breaking of grounding grid occurred in its edge part, in its mid-position as well as in different places simultaneously, thus the variation law of connective resistance of grounding grid under different conditions is obtained.

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A role player for the Lakers a year ago after coming over from Orlando in a trade, Ariza showcased ball-hawking defense and an ability to score in transition in limited playing time before breaking a bone in his right foot in January.

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