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A general private information retrieval scheme for MDS coded databases with colluding servers

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Abstract

The problem of private information retrieval (PIR) gets renewed attentions in recent years due to its information-theoretic reformulation and applications in distributed storage systems. Let M files be stored in a distributed storage system consisting of N servers, where each file is stored via an (N, K)-MDS code. A PIR scheme will allow a user to retrieve a specific file from the distributed storage system without revealing the identity of the file to any T colluding servers. PIR rate is defined as the number of symbols privately retrieved per one downloaded symbol and the supremum of all achievable rates is called the PIR capacity. The capacity has been solved for some degenerate cases, i.e. \(K=1\) or \(T=1\). For the general case \(K\ge 2\) and \(T\ge 2\), the exact PIR capacity remains unknown. In this paper we propose a general private information retrieval scheme for MDS coded databases with colluding servers achieving PIR rate \((1+R+R^2+\cdots +R^{M-1})\), where \(R=1-\frac{{{N-T}\atopwithdelims ()K}}{{N\atopwithdelims ()K}}\). Our scheme captures the essence of the optimal schemes for degenerate cases. We also compare our scheme with some other known PIR schemes for non-degenerate cases. The advantages of our scheme include its independence of the property of the storage code and a better performance when the number of files M is small.

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Acknowledgements

The authors express their gratitude to the two anonymous reviewers for their detailed and constructive comments which are very helpful to the improvement of the presentation of this paper, and to Prof. Tuvi Etzion, the associate editor, for his excellent editorial job.

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  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Yiwei Zhang & Gennian Ge

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  1. Yiwei Zhang
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  2. Gennian Ge
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Correspondence to Gennian Ge.

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Communicated by T. Etzion.

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Yiwei Zhang: Research supported by the Post-Doctoral Science Foundation of China under Grant No. 2017M610942 and Beijing Postdoctoral Research Foundation. Gennian Ge: Research supported by the National Natural Science Foundation of China under Grant Nos. 11431003 and 61571310, Beijing Scholars Program, Beijing Hundreds of Leading Talents Training Project of Science and Technology, and Beijing Municipal Natural Science Foundation.

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Zhang, Y., Ge, G. A general private information retrieval scheme for MDS coded databases with colluding servers. Des. Codes Cryptogr. 87, 2611–2623 (2019). https://doi.org/10.1007/s10623-019-00640-x

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