Semantic watermarking methods enable the direct integration of watermarks into the generation process of latent diffusion models by only modifying the initial latent noise. One line of approaches building on Gaussian Shading relies on cryptographic primitives to steer the sampling process of the latent noise. However, we identify several issues in the usage of cryptographic techniques in Gaussian Shading, particularly in its proof of lossless performance and key management, causing ambiguity in follow-up works, too. In this work, we therefore revisit the cryptographic primitives for semantic watermarking. We introduce a novel, general proof of lossless performance based on IND\$-CPA security for semantic watermarks. We then discuss the configuration of the cryptographic primitives in semantic watermarks with respect to security, efficiency, and generation quality.