TY - JOUR

T1 - A communication-privacy tradeoff for modular addition

AU - Chor, Benny

AU - Kushilevitz, Eyal

N1 - Funding Information:
Correspondence to: B. Chor, Department of Computer Science, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel. * Research supported by US-Israel BSF Grant 88-00282. Email: [email protected]. * * Research supported by ONR-N0001491-J-1981 CCR-90-07677. Email: [email protected].

PY - 1993/3/22

Y1 - 1993/3/22

N2 - We consider the following problem: A set of n parties, each holding an input value xi∈{0, 1,...,m-1}, wishes to distributively compute the sum of their input values modulo the integer m, (i.e, ∑ni=1xi mod m). The parties wish to compute this sum t-privately. That is, in a way that no coalition of size at most t can infer any additional information, other than what follows from their input values and the computed sum. We present an oblivious protocol which computes the sum t-privately, using n·⌈(t+1)/2⌉ messages. This protocol requires fewer messages than the known private protocols for modular addition. Then, we show that this protocol is in a sense optimal, by proving a tight lower bound of ⌈n·(t+1)/2⌉ messages for any oblivious protocol that computes the sum t-privately.

AB - We consider the following problem: A set of n parties, each holding an input value xi∈{0, 1,...,m-1}, wishes to distributively compute the sum of their input values modulo the integer m, (i.e, ∑ni=1xi mod m). The parties wish to compute this sum t-privately. That is, in a way that no coalition of size at most t can infer any additional information, other than what follows from their input values and the computed sum. We present an oblivious protocol which computes the sum t-privately, using n·⌈(t+1)/2⌉ messages. This protocol requires fewer messages than the known private protocols for modular addition. Then, we show that this protocol is in a sense optimal, by proving a tight lower bound of ⌈n·(t+1)/2⌉ messages for any oblivious protocol that computes the sum t-privately.

KW - Distributed computing

KW - message complexity

KW - modular sum

KW - private computation

UR - http://www.scopus.com/inward/record.url?scp=0040655149&partnerID=8YFLogxK

U2 - 10.1016/0020-0190(93)90120-X

DO - 10.1016/0020-0190(93)90120-X

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0040655149

SN - 0020-0190

VL - 45

SP - 205

EP - 210

JO - Information Processing Letters

JF - Information Processing Letters

IS - 4

ER -