Integer Variable chi-Based Ate Pairing

In implementing an efficient pairing calculation, it is saidthat the lower bound of the number of iterations of Miller'salgorithm is log2r/φ(k),where φ(·) is the Euler's function. Ate pairingreduced the number of the loops of Miller's algorithm of Tatepairing from $\lfloor\log_2r\rfloor$ to $\lfloor\log_2(t-1)\rfloor$. Recently, it is known to systematicallyprepare a pairing---friendly elliptic curve whose parameters aregiven by a polynomial of integer variable "Χ". For thecurve, this paper gives integer variable Χ---basedAte pairing that achieves the lower bound byreducing it to $\lfloor\log_2\chi\rfloor$.

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