Private set intersection (PSI) allows participants to securely compute the intersection of their inputs, which has a wide range of applications such as privacy-preserving contact tracing of COVID-19. Most existing PSI protocols were based on asymmetric/symmetric cryptosystem. Therefore, keys-related operations would burden these systems. In this paper, we transform the problem of the intersection of sets into the problem of finding roots of polynomials by using point-value polynomial representation, blind polynomials’ point-value pairs for secure transportation and computation with the pseudorandom function, and then propose an efficient PSI protocol without any cryptosystem. We optimize the protocol based on the permutation-based hash technique which divides a set into multisubsets to reduce the degree of the polynomial. The following advantages can be seen from the experimental result and theoretical analysis: (1) there is no cryptosystem for data hiding or encrypting and, thus, our design provides a lightweight system; (2) with set elements less than 212, our protocol is highly efficient compared to the related protocols; and (3) a detailed formal proof is given in the semihonest model.
Illumina MiSeq high-throughput sequencing technology was used to study the microbial community structure of mediumtemperature Daqu produced via a digitally managed method and the traditional method. The relationship between the changes in physicochemical properties and microorganisms in Daqu during the fermentation process was analyzed. At the end of fermentation, the bacterial diversity of traditional medium-temperature Daqu was higher than that of digital medium-temperature Daqu, and there was no significant difference in the diversity of fungal communities. The dominant bacteria were Weissella, Lactobacillus, Pediococcus and Saccharopolyspora. The dominant fungi were Thermoascus, Issatchenkia and Candia. On the 25th day of fermentation, the bacterial community distribution in the digital Daqu was more even than that in the traditional Daqu, but the fungal community distribution was the opposite. The results of nonmetric multidimensional scale (NMDS) analysis and canonical correlation analysis (CCA) show that Daqu produced by the two fermentation methods had many similarities.
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