Mind Your Nonces Moving
Jiazhe Chen, Mingjie Liu, Hexin Li, Hongsong Shi · 2015
This paper gives a partially-sharing nonces attack on SM2 Digital Signature Algorithm (SM2DSA). Templates, which are built in the scenario of no secrets known, are used to detect the collisions on the Most Significant Byte of the Nonces (MSBN). Targeting a real world smartcard with 8-bit precharged bus, the power consumption of data moving procedure after the random number generation is focused, on which the template building and matching phases are based. With the templates, we obtain a number of pairs of nonces whose first bytes are collided, then a lattice attack on SM2DSA is proposed to recover the private key. Experiments show that our attack works smoothly; our attack is the first implemented lattice attack on SM2DSA in a smartcard, which can also be extended to the other ECC algorithms like ECDSA.