The Kernel Matrix Diffie-Hellman Assumption

We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix \(\mathbf {{A}}\) sampled from some distribution \(\mathcal {D}\), the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of \(\mathbf {{A}}^\top \). This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions.

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