Generalized Framework to Attack RSA with Special Exposed Bits of the Private Key

Shixiong WANG; Longjiang QU; Chao LI; Shaojing FU

doi:10.1587/transfun.E100.A.2113

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Generalized Framework to Attack RSA with Special Exposed Bits of the Private Key

Shixiong WANG, Longjiang QU, Chao LI, Shaojing FU

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Keywords: RSA, partial key exposure attack, lattice, LLL algorithm, Coppersmith's method, unravelled linearization

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2017 Volume E100.A Issue 10 Pages 2113-2122

DOI https://doi.org/10.1587/transfun.E100.A.2113

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Abstract

In this paper, we study partial key exposure attacks on RSA where the number of unexposed blocks of the private key is greater than or equal to one. This situation, called generalized framework of partial key exposure attack, was first shown by Sarkar [22] in 2011. Under a certain condition for the values of exposed bits, we present a new attack which needs fewer exposed bits and thus improves the result in [22]. Our work is a generalization of [28], and the approach is based on Coppersmith's method and the technique of unravelled linearization.

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