Integer-interval means the set of the left and right endpoints of the interval (which are integers) and all integers between them. The positional relationship between integer-intervals is the relation between the positions of two integer-intervals. Aiming at the positional relationship between integer-intervals, a secure two-party computation problem was proposed, in other words, a private-preserving determination problem of integer-interval positional relationship was proposed. In this problem, two users with private-preserving integer-intervals were helped to correctly determine the positional relationship between the two integer-intervals of them with the private preserved. Six positional relationships between two integer-intervals were defined, the 0-1 coding scheme of integer-intervals was given, and a determination rule for integer-interval positional relationship was proved. Then, based on the Goldwasser-Micali cryptosystem and semi-honest attacker model, a secure two-party computation protocol for solving the private-preserving determination problem of integer-interval positional relationship was designed. The protocol was proved to be both correct and secure, and the performance of the protocol was analyzed and explained.

The determination of the relationship between integer point and integer interval in the sense of privacy preserving is an important secure multi-party computation problem, but there are some defects in the existing solutions, such as low efficiency, privacy disclosure, and even possible wrong determination. Aiming at these defects, an improved secure two-party computation protocol for solving this determination problem was constructed. Firstly, analysis of the existing protocols was given and some shortcomings of the protocols were pointed out. Secondly, a new 0-1 coding rule for integer point and integer interval was defined, based on this, a necessary and sufficient condition for an integer point belonging to an integer interval was proved. Finally, by using the necessary and sufficient condition as the determination standard, a secure two-party computation protocol for determining wether the integer point belonging to the integer interval was proposed based on the Goldwasser-Micali encryption system, and its correctness and the security under the semi-honest model were proved. Analysis shows that compared with the existing solutions, the proposed protocol has better privacy preserving feature and will not output wrong results, in addition, both the computation complexity and the communication complexity of the protocol are reduced by about half while the round complexity remains the same.

DNA sequences carry important biological information of human bodies, how to compare multiple DNA sequences correctly with privacy preserving is an important problem. To a certain extent, Hamming distance characterizes the similarity between two DNA sequences. Therefore, the privacy preserving Hamming distance computing problem of DNA sequences was researched. First of all, the "0-1 Coding" of the DNA sequence was defined, which codes the DNA sequence with length n to a 0-1 string with length 4n, proving that the Hamming distance of two DNA sequences is a half of the Hamming distance of their "0-1 Coding" strings. Then, with the help of this conclusion, with the Goldwasser-Micali (GM) encryption algorithm taken as main encryption tool, a secure two-party computation protocol for computing the Hamming distance of two DNA sequences was proposed. It was shown that the protocol is both secure and correct under semi-honest attacker model. The proof of security based on a simulator was given. After then, the efficiency of the protocol was analyzed.

Data scheduling strategy in Peer-to-Peer (P2P) media streaming is the key research of the P2P media streaming system. A Particle Swarm Optimization （PSO） algorithm was modified according to P2P streaming data scheduling features and the style of digital encoding string for the algorithm was proposed in this paper. The data scheduling strategy to choose the data chunk took account of resource urgency and scarcity degree. The modified discrete particle swarm algorithm was used to choose the peers to get the optimal scheduling peers set. In order to verify the feasibility and effectiveness of the algorithm, experiments were done to simulate the convergence of the algorithm, the scheduling time, the P2P network uplink bandwidth utilization and the load balancing of peers.