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Pairings, or bilinear maps, have indeed found a great deal of applications in crypto; hence, researchers have soon pointed out that further "degrees" of linearity (trilinear maps, etc.) would provide even more powerful applications. Nowadays, multilinear maps are one of the most powerful cryptographic primitives. They are at the heart of ...


Select random element from $G-\{1\}$ and call it $g'$. So $order(g')\in\{s\times n',s,n' \}$. case1: $g=n'\cdot g'$ and $φ =s\cdot g'$. case2: $g= g'$. case3: $φ =g'$. repeat above method until $g,φ$ be found.

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