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In Advances in Cryptology – ASIACRYPT 2011, Vol. 7073 (2011), pp. 504-519, doi:10.1007/978-3-642-25385-0_27 Key: citeulike:12080133
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We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field $\mathbbF_q$ of large characteristic from $\widetildeO(\log^8 q)$ to $\widetildeO(\log^5 q)$ . Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian.
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