Partial key exposure attack on RSA using some private key blocks

RSA is a well-known cryptosystem in public-key cryptography and the strength of the cryptosystem depends on the hardness of factoring large integers. Several attacks have been proposed by using the partial information of the secret parameters, which can be obtained by side-channel attacks. Partial key exposure attacks exploit the information gained by a side-channel attack(s) and identify the potential of the RSA cryptosystem if an attacker knows that partial information. In this paper, we investigate the strength of RSA, if an attacker obtains some blocks of the secret exponent, and by guessing successfully a few most significant bits (MSBs) of any of the primes in RSA. Some blocks of the secret exponent can be extracted by cold boot attack and some MSBs of any of the primes can be guessed correctly. We apply LLL algorithm to attack the RSA and follow the Jochemsz and May approach to construct the lattice.