Chair for Embedded Security – Prof. Dr.-Ing. Christof Paar

Elliptic curves have become widespread in cryptographic applications since they offer the same cryptographic functionality as public-key cryptosystems designed over integer rings while needing a much shorter bitlength. The resulting speedup in computation as well as the smaller storage needed for the keys, are reasons to favor elliptic curves. Nowadays, elliptic curves are employed in scenarios which affect the majority of people, such as protecting sensitive data on passports or securing the network communication used, for example, in online banking applications. This works analyzes the security of elliptic curves by practically attacking the very basis of its mathematical security — the Elliptic Curve Discrete Logarithm Problem (ECDLP) — of a binary field curve with a bitlength of 113. As our implementation platform, we choose the RIVYERA hardware consisting of multiple Field Programmable Gate Arrays (FPGAs) which will be united in order to perform the strongest attack known in literature to defeat generic curves: the parallel Pollard’s rho algorithm. Each FPGA will individually perform a what is called additive random walk until two of the walks collide, enabling us to recover the solution o