1
Abstract:
Abstract. Let E/Fp be an elliptic curve, and G E/Fp. Define the Di#e--Hellman function as DHE,G (aG, bG) = abG. We show that if there is an e#cient algorithm for predicting the LSB of the x or y coordinate of abG given #E, G, aG, bG # for a certain family of elliptic curves, then there is an algorithm for computing the Di#e--Hellman function on all curves in this family. This seems stronger than the best analogous results for the Di#e--Hellman function in F # p. Boneh and Venkatesan showed that in F # p computing approximately (log p)
Citations
| 105 | RSA and Rabin functions: certain parts are as hard as the whole – Alexi, Chor, et al. - 1984 |
| 78 | Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related – Boneh, Venkatesan - 1996 |
| 50 | The Decision Die-Hellman Problem – Boneh - 1998 |
| 10 | The modular inversion hidden number problem – Boneh, Halevi, et al. - 2001 |
