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It is well known that if the higher half bits of a prime factor are known or the secret key is small enough then the RSA cryptosystem is broken (e.g. [Coppersmith, J. Cryptology, 1997] and [Boneh-Durfee, Eurocrypt'99]). Recently, Sarkar-Maitra-Sarkar [Cryptology ePrint Archiv, 2008/315] proposed attacks against RSA under the conditions that the higher bits of a prime factor is known and the secret key is small. In the present paper, the authors improve their attacks to be effective for larger secret keys.
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