Random self-reducibility and bit security of the elliptic curve Diffie–Hellman secret keys
نویسندگان
چکیده
We prove that if one can predict the least significant bit of the Diffie–Hellman secret keys for elliptic curves with non-negligible advantage on a polynomial fraction of all curves over a given finite field Fp, then one can compute the entire Diffie–Hellman secret on a polynomial fraction of all curves over the same finite field. Our method combines rapid mixing properties of certain isogeny graphs, results due to Boneh and Shparlinski and a new refinement of H. Lenstra’s lower bounds on the size of an isogeny classes corresponding to almost all traces of the Frobenius.
منابع مشابه
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