This study revisits the side‐channel security of the elliptic curve cryptography (ECC) scalar multiplication implemented with Montgomery ladder. Focusing on a specific implementation that does not use the y ‐coordinate for point addition (ECADD) and point doubling (ECDBL), the authors show that Montgomery ladder on Weierstrass curves is vulnerable to a chosen base‐point attack. Unlike the normal implementation with y ‐coordinate, in the scenario of this study, the chosen base‐point strategy will not lead to operations with two same inputs during the ECADD and/or ECDBL. Instead, by choosing a suitable base‐point, one will find that there are operations that share a common operand; while it is not the case if the base‐point is not chosen correctly. This results in the recovery of the secret (fixed) scalar. They also experiment the methods of shared operand detection on a real‐world SoC, where a secp256k1 dedicated Montgomery ladder scalar multiplication with x ‐only coordinate is implemented, to show the efficiency of the scalar recovery attack. Naturally, the attack can be generalised to other Weierstrass curves when they contain special points.

Low Entropy Masking Schemes (LEMS) are countermeasure techniques to mitigate the high performance overhead of masked hardware and software implementations of symmetric block ciphers by reducing the entropy of the mask sets. The security of LEMS depends on the choice of the mask sets. Previous research mainly focused on searching balanced mask sets for hardware implementations. In this paper, we find that those balanced mask sets may have vulnerabilities in terms of absolute difference when applied in software implemented LEMS. The experiments verify that such vulnerabilities certainly make the software LEMS implementations insecure. To fix the vulnerabilities, we present a selection criterion to choose the mask sets. When some feasible mask sets are already picked out by certain searching algorithms, our selection criterion could be a reference factor to help decide on a more secure one for software LEMS.

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.