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Side Channel Attacks are known to be effective in cracking secret keys utilized in smart cards, electronic passports, and e-ID cards. A combination of masking and shuffling methods has been proposed as a practical countermeasure to such attacks. Using a template attack (TA), S. Tillich recently analyzed an AES using masking and shuffling techniques with a biased-mask attack technique. To apply this method, however, we need to collect the template information on the masking value in advance. Moreover, this method requires knowing the exact time position of the target masking value for a higher probability of success. In this paper, we suggest a new practical method called a Biasing Power Analysis (BPA) to find a secret key used in an AES based on a masking-shuffling method without the use of the time position and template information of the masking value. We conducted an experiment on a BPA attack against a 128-bit AES secret key based on a masking-shuffling method operating on an MSP430 chip and succeeded in finding the entire secret key. The results of this study can be utilized for next-generation ID cards to verify their physical safety.