TY - JOUR
T1 - Efficient Recovery of a Shared Secret via Cooperation
T2 - Applications to SDMM and PIR
AU - Li, Jie
AU - Makkonen, Okko
AU - Hollanti, Camilla
AU - Gnilke, Oliver W.
N1 - Publisher Copyright:
© 1983-2012 IEEE.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - This work considers the problem of privately outsourcing the computation of a matrix product over a finite field {\mathbb {F}}_{q} to N helper servers. These servers are considered to be honest but curious, i.e., they behave according to the protocol but will try to deduce information about the user's data. Furthermore, any set of up to X servers is allowed to share their data. Previous works considered this collusion a hindrance and the download cost of the schemes increases with growing X. We propose to utilize such linkage between servers to the user's advantage by allowing servers to cooperate in the computational task. This leads to a significant gain in the download cost for the proposed schemes. The gain naturally comes at the cost of increased communication load between the servers. Hence, the proposed cooperative schemes can be understood as outsourcing both computational cost and communication cost. Both information-theoretically secure and computationally secure schemes are considered, showing that allowing information leakage that is computationally hard to utilize will lead to further gains. The proposed server cooperation is then exemplified for specific secure distributed matrix multiplication (SDMM) schemes and linear private information retrieval (PIR). Similar ideas naturally apply to many other use cases as well, but not necessarily always with lowered costs.
AB - This work considers the problem of privately outsourcing the computation of a matrix product over a finite field {\mathbb {F}}_{q} to N helper servers. These servers are considered to be honest but curious, i.e., they behave according to the protocol but will try to deduce information about the user's data. Furthermore, any set of up to X servers is allowed to share their data. Previous works considered this collusion a hindrance and the download cost of the schemes increases with growing X. We propose to utilize such linkage between servers to the user's advantage by allowing servers to cooperate in the computational task. This leads to a significant gain in the download cost for the proposed schemes. The gain naturally comes at the cost of increased communication load between the servers. Hence, the proposed cooperative schemes can be understood as outsourcing both computational cost and communication cost. Both information-theoretically secure and computationally secure schemes are considered, showing that allowing information leakage that is computationally hard to utilize will lead to further gains. The proposed server cooperation is then exemplified for specific secure distributed matrix multiplication (SDMM) schemes and linear private information retrieval (PIR). Similar ideas naturally apply to many other use cases as well, but not necessarily always with lowered costs.
KW - Computational security
KW - cooperative SDMM
KW - information-theoretic security
KW - private information retrieval (PIR)
KW - secret sharing
KW - secure distributed matrix multiplication (SDMM)
UR - http://www.scopus.com/inward/record.url?scp=85123275400&partnerID=8YFLogxK
U2 - 10.1109/JSAC.2022.3142366
DO - 10.1109/JSAC.2022.3142366
M3 - Journal article
AN - SCOPUS:85123275400
SN - 0733-8716
VL - 40
SP - 871
EP - 884
JO - IEEE Journal on Selected Areas in Communications
JF - IEEE Journal on Selected Areas in Communications
IS - 3
ER -