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How to Share a Secret

Amos Beimel. How to Share a Secret. Secret Sharing [Shamir79,Blakley79,ItoSaitoNishizeki87]. 1706. 1706. 2 bad. ?. 2538. 3441. 1329. 6634. Applications. Original motivation: Secure storage Building box for cryptographic protocols Secure multiparty computation

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How to Share a Secret

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  1. Amos Beimel How to Share a Secret

  2. Secret Sharing[Shamir79,Blakley79,ItoSaitoNishizeki87] 1706 1706 2 bad ? 2538 3441 1329 6634

  3. Applications • Original motivation: Secure storage • Building box for cryptographic protocols • Secure multiparty computation • Threshold cryptography • Byzantine agreement • Access control • Private information retrieval • Attribute-based encryption • Generalized oblivious transfer BGU - Graduate Day

  4. 2-out-of-2 Secret Sharing Scheme • Input: secret • Choose at random a bit • Share of P1: • Share of P2: BGU - Graduate Day

  5. Shamir’s t-out-of-n Secret Sharing Scheme • Input: secrets • Choose at random apolynomial p(x)=s+r1x+r2x2+…+ rt-1xt-1 • Share of Pj: sj= p(j) s BGU - Graduate Day

  6. Open Question: Generalized Secret Sharing • Not all sets are equal. • There is a collection  of authorized sets • Correctness:Every authorized set can recover s. • Privacy:Every unauthorized set cannot learn s. • Are there efficient schemes for every ? • number of parties: n • Upper bound 2O(n) • Lower bound n2/log n • Open problem: BGU - Graduate Day

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