## Cryptology ePrint Archive: Report 2005/374

Computation of Tate Pairing for Supersingular Curves over characteristic 5 and 7

Kunpeng Wang, Bao Li

Abstract: We compute Tate pairing over supersingular elliptic curves via the generic BGhES\cite{BGES} method for $p=5,7$. In those cases, the point multiplication by $p$ is efficiently computed by the Frobenius endomorphism. The function in a cycle can be efficiently computed by the method of continued fraction.

Category / Keywords: public-key cryptography / Tate pairing, continued fraction, Frobenius Endomorphism, supersingular