论文标题
涵盖了椭圆形曲线的攻击
Cover attacks for elliptic curves with prime order
论文作者
论文摘要
我们为椭圆曲线离散对数问题提供了新的方法。 It is based on a transfer: First an $\mathbb{F}_q$-rational $(\ell,\ell,\ell)$-isogeny from the Weil restriction of the elliptic curve under consideration with respect to $\mathbb{F}_{q^3}/\mathbb{F}_q$ to the Jacobian variety of a genus three curve over $ \ mathbb {f} _q $被应用，然后通过索引 - 钙符号攻击在雅各比安中解决了问题。尽管在所需的同态构建中不使用覆盖地图，但从某种意义上说，这种方法是一种封面攻击。结果，在$ \ tilde {o}（q）$的时间内，可以在$ \ mathbb {f} _ {q^3} $上的一些椭圆曲线组中解决离散对数问题。
We give a new approach to the elliptic curve discrete logarithm problem over cubic extension fields $\mathbb{F}_{q^3}$. It is based on a transfer: First an $\mathbb{F}_q$-rational $(\ell,\ell,\ell)$-isogeny from the Weil restriction of the elliptic curve under consideration with respect to $\mathbb{F}_{q^3}/\mathbb{F}_q$ to the Jacobian variety of a genus three curve over $\mathbb{F}_q$ is applied and then the problem is solved in the Jacobian via the index-calculus attacks. Although using no covering maps in the construction of the desired homomorphism, this method is, in a sense, a kind of cover attack. As a result, it is possible to solve the discrete logarithm problem in some elliptic curve groups of prime order over $\mathbb{F}_{q^3}$ in a time of $\tilde{O}(q)$.
