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New Locally Decodable Codes and Private Information Retrieval Schemes

New Locally Decodable Codes and Private Information Retrieval Schemes. Sergey Yekhanin. LDCs and PIRs.

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New Locally Decodable Codes and Private Information Retrieval Schemes

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  1. New Locally Decodable Codes and Private Information Retrieval Schemes Sergey Yekhanin

  2. LDCs and PIRs Definition: A code C encoding n bits to N bits is called q LDC if every bit of the message can be recovered (w.h.p.) by a randomized decoder reading only q bits of the encoding even after some constant fraction of the encoding has been corrupted. Definition: A q server PIR protocol is a protocol between a user and q non-communicating servers holding an n bit database D, that allows the user to retrieve any bit Di, while leaking no information about i to any server.

  3. LDCs: progress

  4. PIRs: progress

  5. Proof overview Goal: 3 query LDCs of length Exp(n1/3) • Regular Intersecting Families (RIFs) • RIFs yield LDCs • Basic linear-algebraic construction of RIFs • Combinatorial and algebraic niceness of sets • Main construction of RIFs

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