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If such a bilinear map existed then the inherent sequentiality assumption of repeated squaring in RSA groups would not hold. So, the sequentiality assumption of repeated squaring says that one can only compute $f(x)=x^{2^T}\bmod{N}$ by computing $T$ repeated squaring $\bmod N$. Put differently, there is no shortcut when one wants to compute $f(\cdot)$, the ...


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