Weakly-Private Secret Sharing Schemes

Abstract. Secret-sharing schemes are an important tool in cryptography that is used in the construction of many secure protocols. However, the shares’ size in the best known secret-sharing schemes realizing general access structures is exponential in the number of parties in the access structure, making them impractical. On the other hand, the best lower bound known for sharing of an -bit secret with respect to an access structure with n parties is Ω( n/ log n) (Csirmaz, EUROCRYPT 94). No major progress on closing this gap has been obtained in the last decade. Faced by our lack of understanding of the share complexity of secret sharing schemes, we investigate a weaker notion of privacy in secrets sharing schemes where each unauthorized set can never rule out any secret (rather than not learn any “probabilistic” information on the secret). Such schemes were used previously to prove lower bounds on the shares’ size of perfect secret-sharing schemes. Our main results is somewhat...

• Type: Conference
• Year: 2007
• Where: TCC
• Authors: Amos Beimel, Matthew K. Franklin
• Keywords: Access Structure, Cryptography, Secret Sharing Scheme, Secret-sharing Schemes, TCC 2007