Crypto2008-MW (1) - SecureLinearAlgebra...

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    Secure Linear Algebra  against Covert or Unbounded  Adversaries Payman Mohassel    and   Enav Weinreb UC Davis CWI
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    Solving Distributed Linear Constraints                  Privately A 1 x = b 1 A 4 x = b 4 A 3 x = b 3 A 2 x = b 2 output = A 1 A 2 A 3 A 4 x b 1 b 2 b 3 b 4
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    Perfect Matching in Bipartite Graphs E 1 E 2 •  G = (E,V)      E =  E 1   E 2   A G   =   A G 1        A G 2   P 1 P 2 A G 1 A G 2 Det(A G     A G 2 ) =? 0 A is the adjacency matrix of graph G With variables replacing 1’s Det is non-zero, iff G has a perfect matching
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    Problem Secure linear algebra computation Solving linear systems Computing rank, determinant, … Setting Shared  n   matrix/linear system   Multiparty (honest majority) Linear secret sharing Two-party Additive homomorphic encryption Goal Improve round and communication efficiency Defend against stronger adversaries
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    Current Status Multiparty [CKP07] Const. round, O(m + n 2 m) comm. for m  x  n systems Worst case: O(n 4 ) comm. Malicious adversaries (honest majority) [NW06] O(n 0.27 ) rounds, O(n 2 ) comm. Semi-honest adversaries Two-party  [KMWF07] O(logn) rounds, O(n 2 logn) comm. Semi-honest adversaries Yao’s O(1) rounds, O(n 2.38 ) comm.
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    Our Protocols Efficiency For every constant  s O(s)  rounds,  O(sn 2+1/s )  communication Sublinear comm. in circuit complexity   Security Multiparty: malicious adversary (honest  majority)  Two-party: covert adversaries
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Crypto2008-MW (1) - SecureLinearAlgebra...

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