In X-ray computed tomography, scattered X-rays are generally removed by using a post-patient collimator located in front of the detector. In this paper, we show that the scattered X-rays have the potential to improve the estimation accuracy of the attenuation coefficient in computed tomography. In order to clarify the problem, we simplified the geometry of the computed tomography into a thin cylinder composed of a homogeneous material so that only one attenuation coefficient needs to be estimated. We then conducted a Monte Carlo numerical experiment on improving the estimation accuracy of attenuation coefficient by measuring the scattered X-rays with several dedicated toroidal detectors around the cylinder in addition to the primary X-rays. We further present a theoretical analysis to explain the experimental results. We employed a model that uses a T-junction (i.e., T-junction model) to divide the photon transport into primary and scattered components. This division is processed with respect to the attenuation coefficient. Using several T-junction models connected in series, we modeled the case of several scatter detectors. The estimation accuracy was evaluated according to the variance of the efficient estimator, i.e., the Cramer-Rao lower bound. We confirmed that the variance decreases as the number of scatter detectors increases, which implies that using scattered X-rays can reduce the irradiation dose for patients.