TY - JOUR
T1 - Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes
AU - Martinez Peñas, Umberto
PY - 2018/4
Y1 - 2018/4
N2 - Secret-sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q n, where n is the number of shares, and do not provide strong security. In this paper, we give a general framework to construct communication efficient secretsharing schemes based on sequences of nested linear codes, which allows to use, in particular, algebraic geometry codes and allows to obtain strongly secure and communication-efficient schemes. Using this framework, we obtain: 1) schemes with universal and close to optimal communication overheads for arbitrarily large lengths n and a fixed finite field; 2) the first construction of schemes with universal and optimal communication overheads and optimal strong security (for restricted lengths), having, in particular, the component-wise security advantages of perfect schemes and the security and storage efficiency of ramp schemes; and 3) schemes with universal and close to optimal communication overheads and close to optimal strong security defined for arbitrarily large lengths n and a fixed finite field.
AB - Secret-sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q n, where n is the number of shares, and do not provide strong security. In this paper, we give a general framework to construct communication efficient secretsharing schemes based on sequences of nested linear codes, which allows to use, in particular, algebraic geometry codes and allows to obtain strongly secure and communication-efficient schemes. Using this framework, we obtain: 1) schemes with universal and close to optimal communication overheads for arbitrarily large lengths n and a fixed finite field; 2) the first construction of schemes with universal and optimal communication overheads and optimal strong security (for restricted lengths), having, in particular, the component-wise security advantages of perfect schemes and the security and storage efficiency of ramp schemes; and 3) schemes with universal and close to optimal communication overheads and close to optimal strong security defined for arbitrarily large lengths n and a fixed finite field.
KW - secret sharing
KW - algebraic geometry codes
KW - communication efficiency
KW - communication bandwidth
KW - strong security
KW - asymptotic secret sharing
KW - algebraic geometry codes
KW - asymptotic secret sharing
KW - communication bandwidth
KW - communication efficiency
KW - Secret sharing
KW - strong security
UR - http://www.scopus.com/inward/record.url?scp=85045213440&partnerID=8YFLogxK
U2 - 10.1109/TIT.2018.2823326
DO - 10.1109/TIT.2018.2823326
M3 - Journal article
SN - 0018-9448
VL - 64
SP - 4191
EP - 4206
JO - I E E E Transactions on Information Theory
JF - I E E E Transactions on Information Theory
IS - 6
ER -