Linear Algebra with Sub-linear Zero-Knowledge Arguments

We suggest practical sub-linear size zero-knowledge arguments for statements involving linear algebra. Given commitments to matrices over a finite field, we give a sub-linear size zero-knowledge argument that one committed matrix is the product of two other committed matrices. We also offer a sub-linear size zero-knowledge argument for a committed matrix being equal to the Hadamard product of two other committed matrices. Armed with these tools we can give many other sub-linear size zero-knowledge arguments, for instance for a committed matrix being upper or lower triangular, a committed matrix being the inverse of another committed matrix, or a committed matrix being a permutation of another committed matrix. A special case of what can be proved using our techniques is the satisfiability of an arithmetic circuit with

• Type: Conference
• Year: 2009
• Where: CRYPTO
• Authors: Jens Groth
• Keywords: CRYPTO 2009, Cryptology, Size Zero-knowledge Arguments, Sub-linear Size Zero-knowledge, Zero-knowledge Argument