Aside from a brute-force attack, the only one that I know of is the power attack. In this type of attack, the hacker attempts to determine the value of the private key by monitoring the power consumption of a smartcard while it is computing the given cipher text.
The latest in the evolution is called leakage-based differential power analysis (LDPA). This method was created in response to power attack resistant cryptosystems and involves measuring the power leakage during decryption instead of the direct power usage.
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