<p>As an extension of the millionaire problem, the blind millionaire (BM) problem aims to compare the secret sums of participants across different groups while preserving the privacy of individual inputs. It has extensive applications in scenarios such as smart auctions and anonymous voting. However, classical solutions to the BM problem are vulnerable to quantum adversaries with supercomputing capabilities. Existing quantum protocols for the BM problem typically rely on a third party (TP) to compute the exact difference between the sums and announce the comparison result, introducing potential security risks. Furthermore, to protect the secret sums of each group, some protocols often require pre-shared secret keys among participants. This work proposes a quantum protocol with enhanced blindness for the BM problem based on single-qudit states. In our approach, all participants except the TP compute the comparison result by sharing the difference of random numbers. TP in our protocol is solely responsible for quantum state preparation and measurement, with no knowledge of any other information. Security analysis demonstrates that the proposed protocol is resistant to various external or internal attacks.</p>