RSA Key Recovery from Digit Equivalence Information

Abstract

The seminal work of Heninger and Shacham (Crypto 2009) demonstrated a method for reconstructing secret RSA keys from partial information of the key components. In this paper we further investigate this approach but apply it to a different context that appears in some side-channel attacks. We assume a fixed-window exponentiation algorithm that leaks the equivalence between digits, without leaking the value of the digits themselves. We explain how to exploit the side-channel information with the Heninger-Shacham algorithm. To analyse the complexity of the approach, we model the attack as a Markov process and experimentally validate the accuracy of the model. Our model shows that the attack is feasible in the commonly used case where the window size is 5.