Reconstruction and Error Correction of RSA Secret Parameters from the MSB Side

This paper discusses the factorization of the RSA modulus when some ‘partial information’ about the bits of the RSA secret parameters are known. Heninger and Shacham (Crypto 2009) considered the reconstruction of RSA secret parameters from a few randomly known bits, and Henecka, May and Meurer (Crypto 2010) studied the reconstruction of secret parameters when all the bits are known with some probability of error. Both the approaches attempted reconstruction from the least significant side of the parameters. In this paper we provide two new techniques for reconstruction and error correction that work from the most significant side of the parameters. Our idea uses adaptive filtering using a ‘sliding window’ technique. We provide theoretical as well as experimental results that are competitive with the existing works.