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In this paper, the authors present a new algorithm to attack lattice based cryptosystems by solving a problem over real numbers. In the case of the NTRU cryptosystem, if they assume the additional information on the modular operations, they can break the NTRU cryptosystems completely by getting the secret key. They believe that this fact was not known before. Latticed-based cryptosystems are one of the main families of post-quantum cryptosystems. It is currently a public key scheme considered for practical applications, and is now an IEEE 1363.1 Standard.
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