RSA and elliptic curve least significant bit security

Abstract

The security of the least significant bit (LSB) of the secret key in the Elliptic Curve Diffie-Hellman protocol (and of the message in the RSA) is related to the security of the whole key (and of the whole message, respectively). Algorithms to invert these cryptographic algorithms, making use of oracles that predict the LSB, have been published. We implement two of these algorithms, identify critical parameters, and modify the sampling to achieve a significant improvement in running times.