We present a novel technique within the MPC-in-the-Head framework, aiming to design efficient zero-knowledge protocols and digital signature schemes. The technique allows for the simultaneous use of additive and multiplicative sharings of secret information, enabling efficient proofs of linear and multiplicative relations. The applications of our technique are manifold. It is first applied to construct zero-knowledge arguments of knowledge for Double Discrete Logarithms. The resulting protocol achieves improved communication complexity without compromising efficiency. We also propose a new zero-knowledge argument of knowledge for the Permuted Kernel Problem. Eventually, we propose a short (candidate) post-quantum digital signature scheme constructed from a new one-way function based on simple polynomials known as fewnomials. This scheme offers simplicity and ease of implementation.