Horizontal Correlation Analysis of Elliptic Curve Diffie Hellman

Abstract

The world is facing a new revolutionary technology transition, Internet of things (IoT). IoT systems requires secure connectivity of distributed entities, including in-field sensors. For such external devices, Side Channel Analysis poses a potential threat as it does not require complete knowledge about the crypto algorithm. In this work, we perform Horizontal Correlation Power Analysis (HCPA) which is a type of Side Channel Analysis (SCA) over the Elliptic Curve Diffie Hellman (ECDH) key exchange protocol. ChipWhisperer (CW) by NewAE Technologies is an open source toolchain which is utilized to perform the HCPA by using CW toolchain. To best of our knowledge, this is the first attempt to implemented ECDH on Artix-7 FPGA for HCPA. We compare our correlation results with the results from AES -128 bits provided by CW. Our point of attack is the Double and Add algorithm which is used to perform Scalar multiplication in ECC. We obtain a maximum correlation of 7% for the key guess using the HCPA. We also discuss about the possible cause for lower correlation and few potentials ways to improve it. In Addition to HCPA we also perform Simple Power Analysis (SPA) (visual) for ECDH, to guess the trailing zeros in the 128- bit secret key for different power traces.