Lattice-based Homomorphic Signatures¶
Leveraging the construction of a trapdoor, we have:
- Public Key: An uniform random matrix \(A\) and matrices \(C_1, \ldots, C_n\) generated randomly.
- Private Key: The trapdoor corresponding to the matrix \(A\).
As shown in the figure above, the main part of generating a valid signature involves calculating \(R_1, \ldots, R_n\). Given \(C_i\) and \(x_i\), the only way to compute these values is by using the trapdoor for \(A\).