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We introduce a general framework encompassing the main hard problems emerging in lattice-based cryptography, which naturally includes the recently proposed Mersenne prime cryptosystem, but also code-b...
New Protocols for Secure Linear Algebra: Pivoting-Free Elimination and Fast Block-Recursive Matrix Decomposition
secure linear algebra multiparty computation
2018/8/2
Cramer and Damgård were the first to propose a constant-rounds protocol for securely solving a linear system of unknown rank over a finite field in multiparty computation (MPC). For mm linear equ...
MRHS Solver Based on Linear Algebra and Exhaustive Search
Algebraic cryptanalysis MRHS LowMC
2018/1/31
We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher's resis...
Differentially Private Linear Algebra in the Streaming Model
Differential Privacy Linear Algebra Random Projection
2016/1/7
The focus of this paper is a systematic study of differential privacy on streaming data using sketchbased
algorithms. Previous works, like Dwork et al. (ICS 2010, STOC 2010), explored random sampling...
Nearly Sparse Linear Algebra
Sparse Linear Algebra Block Wiedemann Algorithm Discrete Logarithm
2015/12/22
In this article, we propose a method to perform linear algebra
on a matrix with nearly sparse properties. More precisely, although
we require the main part of the matrix to be sparse, we allow some ...
We consider secure delegation of linear algebra computation, wherein a client, \emph{privately} and \emph{verifiably}, outsources tasks such as matrix multiplication, matrix inversion, computing the r...
We consider secure delegation of linear algebra computation, wherein a client, \emph{privately} and \emph{verifiably}, outsources tasks such as matrix multiplication, matrix inversion, computing the r...
We consider secure delegation of linear algebra computation, wherein a client, \emph{privately} and \emph{verifiably}, outsources tasks such as matrix multiplication, matrix inversion, computing the r...
Efficient Zero-knowledge Authentication Based on a Linear Algebra Problem MinRank
Zero-knowledge identification entity authentication
2009/4/16
A Zero-knowledge protocol provides provably secure entity
authentication based on a hard computational problem. Among many
schemes proposed since 1984, the most practical rely on factoring and discr...
Achieving a log(n) Speed Up for Boolean Matrix Operations and Calculating the Complexity of the Dense Linear Algebra step of Algebraic Stream Cipher Attacks and of Integer Factorization Methods
Matrix Inversion Matrix Multiplication Boolean Matrices
2008/11/20
The purpose of this paper is to calculate the running time of dense boolean matrix operations,
as used in stream cipher cryptanalysis and integer factorization. Several variations of Gaussian
Elimin...