TY - GEN
T1 - Secret sharing with public reconstruction
AU - Beimel, Amos
AU - Chor, Benny
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1995.
PY - 1995/1/1
Y1 - 1995/1/1
N2 - All known constructions of information theoretic t-out-of-n secret sharing schemes require secure, private communication channels among the parties for the reconstruction of the secret. In this work we investigate the cost of performing the reconstruction over public communication channels. A naive implementation of this task distributes O(n) one times pads to each party. This results in shares whose size is O(n) times the secret size. We present three implementations of such schemes that are substantially more efficient: A scheme enabling multiple reconstructions of the secret by different subsets of parties, with factor O(n/t) increase in the shares’ size. A one-time scheme, enabling a single reconstruction of the secret, with O(log(n/t)) increase in the shares’ size. A one-time scheme, enabling a single reconstruction by a set of size exactly t, with factor O(1) increase in the shares’ size. We prove that the first implementation is optimal (up to constant factors) by showing a tight Ω(n/t) lower bound for the increase in the shares’ size.
AB - All known constructions of information theoretic t-out-of-n secret sharing schemes require secure, private communication channels among the parties for the reconstruction of the secret. In this work we investigate the cost of performing the reconstruction over public communication channels. A naive implementation of this task distributes O(n) one times pads to each party. This results in shares whose size is O(n) times the secret size. We present three implementations of such schemes that are substantially more efficient: A scheme enabling multiple reconstructions of the secret by different subsets of parties, with factor O(n/t) increase in the shares’ size. A one-time scheme, enabling a single reconstruction of the secret, with O(log(n/t)) increase in the shares’ size. A one-time scheme, enabling a single reconstruction by a set of size exactly t, with factor O(1) increase in the shares’ size. We prove that the first implementation is optimal (up to constant factors) by showing a tight Ω(n/t) lower bound for the increase in the shares’ size.
UR - https://www.scopus.com/pages/publications/84876160772
U2 - 10.1007/3-540-44750-4_28
DO - 10.1007/3-540-44750-4_28
M3 - Conference contribution
AN - SCOPUS:84876160772
SN - 3540602216
SN - 9783540602217
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 353
EP - 366
BT - Advances in Cryptology ― CRYPTO 1995 - 15th Annual International Cryptology Conference, Proceedings
A2 - Coppersmith, Don
PB - Springer Verlag
T2 - 15th Annual International Cryptology Conference, CRYPTO 19995
Y2 - 27 August 1995 through 31 August 1995
ER -