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Aiming at the problem that the fully homomorphic encryption scheme based on single identity cannot satisfy the homomorphic operation of ciphertext under different identities, as well as the inefficiency of trapdoor function and the complexity of sampling algorithm, an improved lattice MIBFHE scheme was proposed. Firstly, we combined MP12 trapdoor function with dual LWE algorithm to construct a new IBE scheme under the standard model, and prove that the scheme is IND-sID-CPA security under the selective identity. Secondly, we used the eigenvector method to eliminate the evaluation key, and transform the above efficient IBE scheme into a single identity IBFHE scheme to satisfy the homomorphic operation. Finally, we improved the ciphertext extension method of CM15 and constructed a new Link-mask system that supports the transformation of IBFHE scheme under the standard model, and then, converted the above IBFHE scheme into MIBFHE scheme based on this system. The comparative analysis results showed that the efficiency of this scheme is improved compared with similar schemes in the trapdoor generation and preimage sampling, and the dimension of lattice and ciphertext size are significantly shortened.

The kinetics of the isothermal reduction of iron ore–coke, iron ore–charcoal, and iron ore–biomass (straw) composite pellets were studied at 900–1200 °C. Compared with the other two composite pellets, the composite pellet using biomass as a reducing agent showed a more rapid reduction rate at a relatively low temperature. With an increase in the temperature, the reduction rates of the three different composite pellets tended to be equal. The reducing reactions of the three different composite pellets were all mainly controlled by gasification diffusion. The reduction rates can be described by the interface reaction kinetic model ([1−(1−m)1/3]2=kt). The apparent activation energies of the gasification diffusion of coke, charcoal, and biomass composite pellets at 900–1200 °C were calculated using the Arrhenius equation, and they were 95.81, 71.67, and 58.69 kJ/mol, respectively. The biomass composite pellets exhibited a lower apparent activation energy than the composite pellets with other reduction agents.

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