TY - GEN
T1 - Lossy chains and fractional secret sharing
AU - Ishai, Yuval
AU - Kushilevitz, Eyal
AU - Strulovich, Omer
PY - 2013
Y1 - 2013
N2 - Motivated by the goal of controlling the amount of work required to access a shared resource or to solve a cryptographic puzzle, we introduce and study the related notions of lossy chains and fractional secret sharing. Fractional secret sharing generalizes traditional secret sharing by allowing a fine-grained control over the amount of uncertainty about the secret. More concretely, a fractional secret sharing scheme realizes a fractional access structure f: 2[n] ! {0,.,m - 1} by guaranteeing that from the point of view of each set T ⊆ [n] of parties, the secret is uniformly distributed over a set of f(T) + 1 potential secrets. We show that every (monotone) fractional access structure can be realized. For symmetric structures, in which f(T) depends only on the size of T, we give an efficient construction with share size poly(n, logm). Our construction of fractional secret sharing schemes is based on the new notion of lossy chains which may be of independent interest. A lossy chain is a Markov chain (X0,.,Xn) which starts with a random secret X0 and gradually loses information about it at a rate which is specified by a loss function g. Concretely, in every step t, the distribution of X0 conditioned on the value of Xt should always be uniformly distributed over a set of size g(t). We show how to construct such lossy chains efficiently for any possible loss function g, and prove that our construction achieves an optimal asymptotic information rate.
AB - Motivated by the goal of controlling the amount of work required to access a shared resource or to solve a cryptographic puzzle, we introduce and study the related notions of lossy chains and fractional secret sharing. Fractional secret sharing generalizes traditional secret sharing by allowing a fine-grained control over the amount of uncertainty about the secret. More concretely, a fractional secret sharing scheme realizes a fractional access structure f: 2[n] ! {0,.,m - 1} by guaranteeing that from the point of view of each set T ⊆ [n] of parties, the secret is uniformly distributed over a set of f(T) + 1 potential secrets. We show that every (monotone) fractional access structure can be realized. For symmetric structures, in which f(T) depends only on the size of T, we give an efficient construction with share size poly(n, logm). Our construction of fractional secret sharing schemes is based on the new notion of lossy chains which may be of independent interest. A lossy chain is a Markov chain (X0,.,Xn) which starts with a random secret X0 and gradually loses information about it at a rate which is specified by a loss function g. Concretely, in every step t, the distribution of X0 conditioned on the value of Xt should always be uniformly distributed over a set of size g(t). We show how to construct such lossy chains efficiently for any possible loss function g, and prove that our construction achieves an optimal asymptotic information rate.
KW - Cryptography
KW - Markov chains
KW - Secret sharing
UR - http://www.scopus.com/inward/record.url?scp=84892562384&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.STACS.2013.160
DO - 10.4230/LIPIcs.STACS.2013.160
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:84892562384
SN - 9783939897507
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 160
EP - 171
BT - 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013
T2 - 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013
Y2 - 27 February 2013 through 2 March 2013
ER -