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International Association for Cryptologic Research (IACR)
Abstract
We investigate a lattice construction method for the Coppersmith technique
for finding small solutions of a modular equation.
We consider its variant for simultaneous equations
and propose a method to construct a lattice
by combining lattices for solving single equations.
As applications,
we consider
a new RSA cryptanalyses.
Our algorithm can factor an RSA modulus from ββ₯2 pairs of RSA public exponents with the common modulus
corresponding to secret exponents smaller than N(9ββ5)/(12β+4),
which improves on the previously best known result by Sarkar and Maitra.
For partial key exposure situation,
we also can factor the modulus if
Ξ²βΞ΄/2+1/4<(3ββ1)(3β+1),
where Ξ² and Ξ΄ are bit-lengths /logN of the secret exponent and its exposed LSBs,
respectively
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