This paper presents a security evaluation of the RRSC lightweight stream cipher in its 64-bit and 128-bit variants. The analysis examines the key update process, internal component interactions, and diffusion behavior during initialization, supported by an avalanche study. Based on these observations, several cryptanalytic scenarios are explored, including time-memory-data trade-off attacks, full key-recovery attacks in the known-plaintext setting, and partial key-recovery attacks targeting the linear feedback shift register and nonlinear feedback shift register components. It is shown that the effective key space is reduced from (2^{128}) to (2^{96}) for the 128-bit variant and from (2^{64}) to (2^{48}) for the 64-bit variant.