Communication Efficient Secure Linear Algebra
نویسندگان
چکیده
We present communication efficient secure protocols for a variety of linear algebra problems. Our main building block is a protocol for computing Gaussian Elimination on encrypted data. As input for this protocol, Bob holds a k×k matrix M , encrypted with Alice’s key. At the end of the protocol run, Bob holds an encryption of an upper-triangular matrix M ′ such that the number of nonzero elements on the diagonal equals the rank of M . The communication complexity of our protocol is roughly O(k). Building on Oblivious Gaussian elimination, we present secure protocols for several problems: deciding the intersection of linear and affine subspaces, picking a random vector from the intersection, and obliviously solving a set of linear equations. Our protocols match known (insecure) communication complexity lower bounds, and improve the communication complexity of both Yao’s garbled circuits and that of specific previously published protocols.
منابع مشابه
A Note on Secure Computation of the Moore-Penrose Pseudoinverse and Its Application to Secure Linear Algebra
This work deals with the communication complexity of secure multi-party protocols for linear algebra problems. In our model, complexity is measured in terms of the number of secure multiplications required and protocols terminate within a constant number of rounds of
متن کاملSecure Linear Algebra Using Linearly Recurrent Sequences
In this work we present secure two-party protocols for various core problems in linear algebra. Our main result is a protocol to obliviously decide singularity of an encrypted matrix: Bob holds an n×n matrix, encrypted with Alice’s secret key, and wants to learn whether or not the matrix is singular (while leaking nothing further). We give an interactive protocol between Alice and Bob that solv...
متن کاملSecure Efficient Multiparty Computing of Multivariate Polynomials and Applications
We present a robust secure methodology for computing functions that are represented as multivariate polynomials where parties hold different variables as private inputs. Our generic efficient protocols are fully black-box and employ threshold additive homomorphic encryption. They do not assume honest majority, yet are robust and can detect any misbehavior. We achieve a solution that both, takes...
متن کاملEfficient Secure Linear Algebra in the Presence of Covert or Computationally Unbounded Adversaries
In this work we study the design of secure protocols for linear algebra problems. All current solutions to the problem are either inefficient in terms of communication complexity or assume that the adversary is honest but curious. We design protocols for two different adversarial settings: First, we achieve security in the presence of a covert adversary, a notion recently introduced by [Aumann ...
متن کاملEfficient and Secure Delegation of Linear Algebra
We consider secure delegation of linear algebra computation, wherein a client, privately and verifiably, outsources tasks such as matrix multiplication, matrix inversion, computing the rank and determinant, and solving a linear system to a remote worker. When operating on n×n matrices, we design non-interactive, and secure protocols for delegating matrix multiplication, based on a number of enc...
متن کامل