Private information retrieval in distributed storage systems using an arbitrary linear code

Abstract

We propose an information-theoretic private information retrieval (PIR) scheme for distributed storage systems where data is stored using a linear systematic code of rate R > 1/2. The proposed scheme generalizes the PIR scheme for data stored using maximum distance separable codes recently proposed by Tajeddine and El Rouayheb for the scenario of a single spy node. We further propose an algorithm to optimize the communication price of privacy (cPoP) using the structure of the underlying linear code. As an example, we apply the proposed algorithm to several distributed storage codes, showing that the cPoP can be significantly reduced by exploiting the structure of the distributed storage code.

Private information retrieval from MDS coded data with colluding servers: Settling a conjecture by Freij-Hollanti et al

“…Claim. The C n satisfying the two required properties exist over F p for a sufficiently large prime p. 8 Proof: This proof of existence will use Schwartz-Zippel lemma [9,10] about the roots of a polynomial. The variables for the polynomial are the coefficients of the C n matrices.…”

SoK of Used Cryptography in Blockchain

“…PIR requires an adequate amount of processing, but in the future there might be efficient PIR techniques which can be implemented in blockchain. PIR has also been applied in distributed storage [182] which can be further investigated and adopted in blockchain.…”

The Capacity of Multi-round Private Information Retrieval from Byzantine Databases

“…1 and x j2 2 , due to the use of the (48,16)-MDS code. By calculating a j2 [1:24] and b j2 [1:24] according to (5) and (6) :24] with the corresponding Block j 2 received from the six databases in Round 1. This comparison will for sure reveal the identify of the uncaught byzantine database as it had introduced at least one error in this block.…”