Evaluating the Cache Side Channel Attacks Against ECDSA

Various attacks are proposed against different ECDSA implementations: the key-related data are acquired through cache side channels, and then processed to recover the private key. For each cache side channel attack, the requirements of the data qualified for sequent processing vary greatly, and the success probability of private key recovery relies on both the acquired data and the parameters of data processing. So it is difficult to tell, for a certain ECDSA implementation, (a) how many signatures does a cache side channel attack need to recover the private key? or which attack performs the best? and (b) what kind of threat level exists due to potential side channel attacks, if the ECDSA implementation runs for a number of signatures on an unprotected system with cache side channels? Currently, there is no quantitative metric to fairly answer the questions. Such a metric to evaluate cache side channel attacks, will provide a reference for the adversaries to choose the suitable attack, and also for the defenders to set up protections for the certain ECDSA implementation (e.g., updating the private key after it has been used for a certain number of signatures). In this paper, we design an evaluation approach to quantitatively compare the cache side channel attacks against ECDSA. The expected minimum number of signatures needed for at least one successful private key recovery, is proposed as the metric, and this metric considers both the data requirements and the success probability. We apply the approach to evaluate various cache side channel attacks against ECDSA. By calculating the metric, we obtain (a) for each attack, the optimal parameters with the minimum number of signatures needed, and (b) for each ECDSA implementation, the minimum number of signatures that will be enough for at least one successful private key recovery of some cache side channel attacks.