TY - GEN

T1 - Evolving ramp secret-sharing schemes

AU - Beimel, Amos

AU - Othman, Hussien

N1 - Funding Information:
Research supported by ISF grant 152/17, the BGU Cyber Security Research Center, and by the Frankel center for computer science.
Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Evolving secret-sharing schemes, introduced by Komargodski, Naor, and Yogev (TCC 2016b), are secret-sharing schemes in which the dealer does not know the number of parties that will participate. The parties arrive one by one and when a party arrives the dealer gives it a share; the dealer cannot update this share when other parties arrive. Komargodski and Paskin-Cherniavsky (TCC 2017) constructed evolving a· i -threshold secret-sharing schemes (for every 0 < a< 1), where any set of parties whose maximum party is the i-th party and contains at least ai parties can reconstruct the secret; any set such that all its prefixes are not an a-fraction of the parties should not get any information on the secret. The length of the share of the i-th party in their scheme is O(i4log i). As the number of parties is unbounded, this share size can be quite large. In this work we suggest studying a relaxation of evolving threshold secret-sharing schemes; we consider evolving (a, b)-ramp secret-sharing schemes for 0 < b< a< 1. Again, we require that any set of parties whose maximum party is the i-th party and contains at least ai parties can reconstruct the secret; however, we only require that any set such that all its prefixes are not a b-fraction of the parties should not get any information on the secret. For all constants 0 < b< a< 1, we construct an evolving (a, b)-ramp secret-sharing scheme where the length of the share of the i-th party is O(1). Thus, we show that evolving ramp secret-sharing schemes offer a big improvement compared to the known constructions of evolving a· i -threshold secret-sharing schemes.

AB - Evolving secret-sharing schemes, introduced by Komargodski, Naor, and Yogev (TCC 2016b), are secret-sharing schemes in which the dealer does not know the number of parties that will participate. The parties arrive one by one and when a party arrives the dealer gives it a share; the dealer cannot update this share when other parties arrive. Komargodski and Paskin-Cherniavsky (TCC 2017) constructed evolving a· i -threshold secret-sharing schemes (for every 0 < a< 1), where any set of parties whose maximum party is the i-th party and contains at least ai parties can reconstruct the secret; any set such that all its prefixes are not an a-fraction of the parties should not get any information on the secret. The length of the share of the i-th party in their scheme is O(i4log i). As the number of parties is unbounded, this share size can be quite large. In this work we suggest studying a relaxation of evolving threshold secret-sharing schemes; we consider evolving (a, b)-ramp secret-sharing schemes for 0 < b< a< 1. Again, we require that any set of parties whose maximum party is the i-th party and contains at least ai parties can reconstruct the secret; however, we only require that any set such that all its prefixes are not a b-fraction of the parties should not get any information on the secret. For all constants 0 < b< a< 1, we construct an evolving (a, b)-ramp secret-sharing scheme where the length of the share of the i-th party is O(1). Thus, we show that evolving ramp secret-sharing schemes offer a big improvement compared to the known constructions of evolving a· i -threshold secret-sharing schemes.

UR - http://www.scopus.com/inward/record.url?scp=85053607261&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-98113-0_17

DO - 10.1007/978-3-319-98113-0_17

M3 - Conference contribution

AN - SCOPUS:85053607261

SN - 9783319981123

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 313

EP - 332

BT - Security and Cryptography for Networks - 11th International Conference, SCN 2018, Proceedings

A2 - Catalano, Dario

A2 - De Prisco, Roberto

PB - Springer Verlag

T2 - 11th International Conference on Security and Cryptography for Networks, SCN 2018

Y2 - 5 September 2018 through 7 September 2018

ER -