We describe a variation of the Schnorr-Lyubashevsky approach to devising signature schemes that is adapted to rank based cryptography. This new approach enables us to obtain a randomization of the signature, which previously seemed difficult to derive for code-based cryptography. We provide a detailed analysis of attacks and an EUF-CMA proof for our scheme. Our scheme relies on the security of the Ideal Rank Support Learning and the Ideal Rank Syndrome problems and a newly introduced problem: Product Spaces Subspaces Indistinguishability, for which we give a detailed analysis. Overall the parameters we propose are efficient and comparable in terms of signature size to the Dilithium lattice-based scheme, with a signature size of 4 kB for a public key of size less than 20 kB.