Bilinear Diffie Sample Clauses

Bilinear Diffie. Xxxxxxx (BDH)) For a, b, c ∈R Zq∗, given (aPi, bPj, cPk), for some values of i, j, k ∈ {1, 2}, computing eˆ(P1, P2)abc is hard. If we wish to make the values of i, j, k explicit we shall refer to this as the BDHi,j,k problem. In the case of Type 1 pairings, i.e., when G1 = G2, this issue of needing to quantify the BDH problem does not arise. It is trivial to show that the BDHi,j,k assumption implies the following Diffie–Xxxxxxx assumption DHi,j,k' when k /= k′. ∈
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Bilinear Diffie. Xxxxxxx (BDH)) For a, b, c ∈R Zq∗, given (aPi, bPj, cPk), for some values of i, j, k ∈ {1, 2}, computing eˆ(P1, P2)abc is hard. If we wish to make the values of i, j, k explicit we shall refer to this as the BDHi,j,k problem. In the case of Type 1 pairings, i.e., when G1 = G2, this issue of needing to quantify the BDH problem does not arise. It is trivial to show that the BDHi,j,k assumption implies the following Diffie–Xxxxxxx assumption DHi,j,kr when k ƒ= kj. ∈ ∈ { } Assumption 2 (Diffie–Xxxxxxx (DH)) For a, b R Zq∗ and some values of i, j, k 0, 0 , xxxxx (xXx, xXx), computing abPk is hard. In some schemes, the following variants of the BDH assumption are used, again we can make them depend explicitly on i, j, k if required.

Related to Bilinear Diffie

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