Multiplier as a Mean for Reducing Vulnerability of Atomic Patterns to Horizontal Address-Bit Attacks

Modern communication systems rely heavily on cryptography to ensure authenticity, confidentiality and integrity of exchanged messages. Elliptic Curve Cryptography is one of the common used standard methods for encrypting and signing messages. In this paper we report on findings for our implementation of an accelerator for elliptic curve P-256 with respect to side channel analysis. First we show that our implementation despite it obeys the atomicity principle is vulnerable to horizontal address-bit differential power analysis that is a single trace attack exploiting key dependent addressing of design's blocks. We used an easy statistical analysis of the trace, the comparison to the mean. This method allows to distinguish tiny differences in shapes of the processing of the ' ‘0’ key bit values from the’ l’ bit values. We applied this method to distinguish the shapes of “point doubling” atomic patterns from the “point addition” atomic patterns. As the atomicity principle is thought to ensure the resistance against such attacks this finding is of utmost importance. Second we introduce the use of dummy operation of the multiplier used as a means to reduce the vulnerability of our hardware accelerator to horizontal attacks. Without dummy partial multiplications, 3 key candidates were revealed with the correctness of 100%,99% and 100%, when the multiplier was not active. When running dummy operations the correctness of the key candidates was reduced down to 95%, 74% and 81% respectively.