Research on ECDSA timing attack based on hidden Markov model

Abstract

Timing attack is a side channel attack method. Elliptic curve cryptography (ECC) is one of the most important publickey cryptography. In this paper, a new timing attack on the Elliptic Curve Digital Signature Algorithm (ECDSA) based on Hidden Markov Model (HMM) was presented. Precisely speaking, the Grover algorithm was used to retrieve the parts of the ephemeral key, and the Koblitz Curve K-409 which was recommended by NIST was attacked successfully. The experiment results showed that the attack could recover almost all the key bits in a few minutes by collecting only once timing dates, and was easy to experiment at a high success rate.