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Isomorphism Classes of Genus2 Hyperelliptic Curves Over Finite Fields
"... We propose a reduced equation for hyperelliptic curves of genus 2 over finite fields F q of q elements with characteristic different from 2 and 5. We determine the number of isomorphism classes of genus2 hyperelliptic curves having an F q rational Weierstrass point. These results have applications ..."
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We propose a reduced equation for hyperelliptic curves of genus 2 over finite fields F q of q elements with characteristic different from 2 and 5. We determine the number of isomorphism classes of genus2 hyperelliptic curves having an F q rational Weierstrass point. These results have applications to hyperelliptic curve cryptography.
The Fault Attack ECDLP Revisited ∗
"... Biehl et al.[2] proposed a faultbased attack on elliptic curve cryptography. In this paper, we refined the fault attack method. An elliptic curve E is defined over prime field Fp with base point P ∈ E(Fp). Applying the fault attack on these curves, the discrete logarithm on the curve can be compute ..."
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Biehl et al.[2] proposed a faultbased attack on elliptic curve cryptography. In this paper, we refined the fault attack method. An elliptic curve E is defined over prime field Fp with base point P ∈ E(Fp). Applying the fault attack on these curves, the discrete logarithm on the curve can be computed in subexponential time of Lp(1/2, 1+o(1)). The runtime bound relies on heuristics conjecture about smooth numbers similar to the ones used in [9].