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- W2594022243 abstract "Recently, Bunder, Nitaj, Susilo and Tonien utilized the continued fraction method to solve for the unknowns of a modular equation which has been applied in three variants of RSA cryptosystem, where the modular equation can be expressed as $$edequiv 1,mathrm {mod},(p^2-1)(q^2-1)$$ and $$N=pq$$ is an RSA modulus. According to their work, when the private key $$d simeq N^{delta }$$ satisfies that $$delta < frac{3-alpha }{2}$$ for $$alpha ge 1$$ , where $$e simeq N^{alpha }$$ , the modulus N can be factored in polynomial time. In this paper, we revisit their work and improve the previous bound to $$delta < 2 - sqrt{alpha }$$ for $$alpha ge 1$$ . More specifically, by utilizing Coppersmith’s method to solve for the unknowns of a modular equation and using unravelled linearization technique in the lattice construction, we can successfully improve their result. Our attack are verified by experiments." @default.
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- W2594022243 date "2017-01-01" @default.
- W2594022243 modified "2023-10-16" @default.
- W2594022243 title "An Improved Analysis on Three Variants of the RSA Cryptosystem" @default.
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- W2594022243 doi "https://doi.org/10.1007/978-3-319-54705-3_9" @default.
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