Secret Sharing from Non-Extractable Randomness
Researchers show two-of-two secret sharing of long secrets does not need extractable randomness.
The paper answers a question left open by Bosley and Dodis (TCC 2007): unlike information-theoretic encryption of long messages, two-out-of-two secret sharing of a long secret does not require extractable randomness. For every b at least 2, the authors build flat sources on b+2 bits, each with min-entropy at least b, and a perfectly correct and private scheme that shares a b-bit secret into two (b+1)-bit shares. Every deterministic map to one bit stays at least statistical distance 1/6 from uniform on some source. The construction extends to two-out-of-n and r-out-of-r sharing with stated extraction-error bounds.
- Negative answer to the TCC 2007 question on two-of-two secret sharing.
- Flat sources of min-entropy at least b share a b-bit secret into two b+1-bit shares.
- No deterministic one-bit extractor is closer than statistical distance 1/6 to uniform.
- Similar perfect schemes are given for two-of-n and r-of-r sharing.
From the original article
1 min read at arxiv.orgBosley and Dodis (TCC 2007) proved that a class of imperfect randomness sources that suffices for information-theoretic encryption of messages longer than the logarithm of the key length must admit deterministic extraction of nearly uniform bits, and asked whether the same is true of two-out-of-two secret sharing.
By Divesh Aggarwal · arxiv.org
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