Acoustic Cryptanalysis: This method involves using sound waves to extract cryptographic keys. Researchers have shown that by analyzing the acoustic emissions of a device, it is possible to infer the internal operations and, consequently, the TPM keys.

Determining which side-channel attack method has the highest chance of success in extracting cryptographic keys from a Trusted Platform Module (TPM) can depend on various factors, including the specific implementation of the TPM, the attacker’s available resources, and the environment in which the attack is carried out. However, some methods generally show higher success rates due to their effectiveness and the breadth of information that can be gleaned from them.

**Power Analysis Attacks (DPA and SPA)**: Power analysis attacks, particularly Differential Power Analysis (DPA), have been proven to be very successful against TPMs and other cryptographic implementations. DPA can work even in the presence of noise and can extract keys from many cryptographic operations. Given that power consumption patterns can be tied closely to the operations being performed, this attack can be highly effective.

**Electromagnetic Analysis (EMA)**: Similar to power analysis, electromagnetic analysis leverages the emissions from the TPM chip while it is performing cryptographic operations. Successful attacks have demonstrated the ability to extract secret keys through careful analysis of these emissions. EMA is often effective because it can reveal internal operations that are not as easily monitored through power consumption.

**Hybrid Attacks**: Hybrid attacks that combine different side-channel techniques, such as power and electromagnetic analysis or power and timing attacks, increase the effectiveness of key extraction significantly. By using multiple vectors, an attacker can corroborate findings and overcome potential weaknesses of single-method approaches.

**Acoustic Cryptanalysis**: Although this method is more niche, certain implementations of devices might be susceptible to this type of analysis. Acoustic emissions can sometimes provide a unique insight into the operations of a device during cryptographic processing.

**Machine Learning-Enhanced Power Attacks**: The integration of machine learning techniques with power analysis attacks has shown promise, particularly against more robust TPM implementations. Machine learning can help in distinguishing subtle differences in power traces that traditional methods might miss.

**Fault Injection Attacks**: While fault injection can be highly effective, its success often depends on the ability to produce reproducible faults in a controlled manner. Non-invasive methods may offer better chances for extraction, but they can still be tricky to execute.

**Timing Attacks and Cache Timing Attacks**: While still relevant, timing attacks generally face challenges in practical implementations, particularly with modern defenses. More sophisticated implementations may include measures to mitigate timing variations.

In summary, **power analysis attacks (particularly DPA)** and **electromagnetic analysis** tend to have the highest chances of success due to their ability to exploit the physical characteristics of the TPM during operation. Hybrid approaches that combine these methods are also highly effective. The actual success will depend on context, preparation, and the measures in place to protect against such attacks.