TY - JOUR

T1 - Towards efficient private distributed computation on unbounded input streams

AU - Dolev, Shlomi

AU - Garay, Juan

AU - Gilboa, Niv

AU - Kolesnikov, Vladimir

AU - Yuditsky, Yelena

N1 - Funding Information:
Funding: This research has been supported by the Israeli Ministry of Science and Technology (MOST), the Institute for Future Defense Technologies Research named for the Medvedi, Shwartzman and Gensler Families, the Israel Internet Association (ISOC-IL), the Lynne and William Frankel Center for Computer Science at Ben-Gurion University, Rita Altura Trust Chair in Computer Science, Israel Science Foundation (grant number 428/11), Cabarnit Cyber Security MAGNET Consortium, MAFAT and Deutsche Telekom Labs at BGU.
Publisher Copyright:
© 2015 by De Gruyter.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - In the problem of private "swarm" computing, n agents wish to securely and distributively perform a computation on common inputs, in such a way that even if the entire memory contents of some of them are exposed, no information is revealed about the state of the computation. Recently, Dolev, Garay, Gilboa and Kolesnikov [Innov. Comput. Sci. (2011), 32-44] considered this problem in the setting of information-theoretic security, showing how to perform such computations on input streams of unbounded length. However, the cost of their solution is exponential in the size of the finite state automaton (FSA) computing the function. In this work we are interested in an efficient (i.e., polynomial time) computation of the above model, at the expense of minimal additional assumptions. Relying on the existence of one-way functions, we show how to process unbounded inputs (polynomial in the security parameter) at a cost linear in m, the number of FSA states. In particular, our algorithms achieve the following: In the case of (n,n)-reconstruction (i.e., in which all n agents participate in the reconstruction of the distributed computation) and at most n - 1 agents are corrupted, the time required to process each input symbol and the time complexity for reconstruction are O(mn), while agent storage is O(m+n). In the case of (n-t,n)-reconstruction (where only n-t agents take part in the reconstruction) and at most t agents are corrupted, the agents' storage is O(n-1n-t) + m), the time required to process each input symbol is O(m(n-1n-t) and the time complexity of reconstruction is O(mt). We achieve the above through a carefully orchestrated use of pseudo-random generators and secret-sharing, and in particular a novel share re-randomization technique which might be of independent interest.

AB - In the problem of private "swarm" computing, n agents wish to securely and distributively perform a computation on common inputs, in such a way that even if the entire memory contents of some of them are exposed, no information is revealed about the state of the computation. Recently, Dolev, Garay, Gilboa and Kolesnikov [Innov. Comput. Sci. (2011), 32-44] considered this problem in the setting of information-theoretic security, showing how to perform such computations on input streams of unbounded length. However, the cost of their solution is exponential in the size of the finite state automaton (FSA) computing the function. In this work we are interested in an efficient (i.e., polynomial time) computation of the above model, at the expense of minimal additional assumptions. Relying on the existence of one-way functions, we show how to process unbounded inputs (polynomial in the security parameter) at a cost linear in m, the number of FSA states. In particular, our algorithms achieve the following: In the case of (n,n)-reconstruction (i.e., in which all n agents participate in the reconstruction of the distributed computation) and at most n - 1 agents are corrupted, the time required to process each input symbol and the time complexity for reconstruction are O(mn), while agent storage is O(m+n). In the case of (n-t,n)-reconstruction (where only n-t agents take part in the reconstruction) and at most t agents are corrupted, the agents' storage is O(n-1n-t) + m), the time required to process each input symbol is O(m(n-1n-t) and the time complexity of reconstruction is O(mt). We achieve the above through a carefully orchestrated use of pseudo-random generators and secret-sharing, and in particular a novel share re-randomization technique which might be of independent interest.

KW - Secure multiparty computation

KW - privacy in computing

UR - http://www.scopus.com/inward/record.url?scp=84930977952&partnerID=8YFLogxK

U2 - 10.1515/jmc-2013-0039

DO - 10.1515/jmc-2013-0039

M3 - Article

AN - SCOPUS:84930977952

SN - 1862-2976

VL - 9

SP - 79

EP - 94

JO - Journal of Mathematical Cryptology

JF - Journal of Mathematical Cryptology

IS - 2

ER -