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BTU
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.
While IoT technology makes industries, cities, and homes smarter, it also opens the door to security risks. With the right equipment and physical access to the devices, the attacker can leverage side-channel information, like timing, power consumption, or electromagnetic emanation, to compromise cryptographic operations and extract the secret key. This work presents a side channel analysis of a cryptographic hardware accelerator for the Elliptic Curve Scalar Multiplication operation, implemented in a Field-Programmable Gate Array and as an Application-Specific Integrated Circuit. The presented framework consists of initial key extraction using a state-of-the-art statistical horizontal attack and is followed by regularized Artificial Neural Networks, which take, as input, the partially incorrect key guesses from the horizontal attack and correct them iteratively. The initial correctness of the horizontal attack, measured as the fraction of correctly extracted bits of the secret key, was improved from 75% to 98% by applying the iterative learning.