Advances in Cryptology - EUROCRYPT 2008
Advances in Cryptology - EUROCRYPT 2008
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密码学进展 - EUROCRYPT 2008
DOI：
10.1007/978-3-540-78967-3_10
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Smith B
中科院分区：
文献类型：
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作者：
Smith B
我们描述了使用显式同源将离散对数问题的实例从超椭圆亏格为3曲线的Jacobian转换为非超椭圆亏格为Fe3曲线的Jacobian，在这种情况下，它们容易受到更快的索引演算攻击。对于特征不大于2或不大于3的域上的任意超椭圆亏格ℤ3曲线，我们给出了核同构于(ℤ/2 )3(在基域的代数闭包上)的同调的显式公式.这些同调对于定义在特征为p>；DLP3的有限域上的所有超椭圆亏格F3曲线的正分部是有理的.在合理的假设下，对于给定有限域上约18.57%的超椭圆亏格3曲线，我们的构造给出了从超椭圆到非超椭圆雅可比的显式有效约简.
We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to (ℤ/2ℤ)3(over an algebraic closure of the base field) for any hyperelliptic genus 3 curve over a field of characteristic not 2 or 3. These isogenies are rational for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristicp> 3. Subject to reasonable assumptions, our constructions give an explicit and efficient reduction of instances of the DLP from hyperelliptic to non-hyperelliptic Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given finite field.