Vulnerability of Atomic Patterns to Simple SCA

In this work we discuss the vulnerability of atomic pattern algorithms for elliptic curve point multiplication against simple side-channel analysis attacks using our own implementation as an example. One of the assumptions, on which the atomicity principle is based, is the indistinguishability of operations with different registers, i.e. storing of the data into two different registers cannot be distinguished if their old and new data values are the same. But before the data can be stored in a register/block, this register/block has to be addressed for storing the data. Different registers/blocks have different addresses. The key-dependent addressing of registers/blocks is an inherent feature of the binary
$kP$
algorithms and allows to reveal the key
$k$
. In our work we demonstrated it. This means that the main assumption, that addressing of different registers/blocks is an indistinguishable operation, may no longer be applied when realizing
$kP$
implementations, at least not for hardware implementations.