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- W1815075800 abstract "We show that the least significant bits (LSB) of the elliptic curve Diffie---Hellman secret keys are hardcore. More precisely, we prove that if one can efficiently predict the LSB with non-negligible advantage on a polynomial fraction of all the curves defined over a given finite field $mathbb{F}_p$, then with polynomial factor overhead, one can compute the entire Diffie---Hellman secret on a polynomial fraction of all the curves over the same finite field. Our approach is based on random self-reducibility (assuming GRH) of the Diffie---Hellman problem among elliptic curves of the same order. As a part of the argument, we prove a refinement of H. W. Lenstra's lower bounds on the sizes of the isogeny classes of elliptic curves, which may be of independent interest." @default.
- W1815075800 created "2016-06-24" @default.
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- W1815075800 date "2008-08-20" @default.
- W1815075800 modified "2023-09-23" @default.
- W1815075800 title "Bits Security of the Elliptic Curve Diffie–Hellman Secret Keys" @default.
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- W1815075800 doi "https://doi.org/10.1007/978-3-540-85174-5_5" @default.
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