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首页> 外文会议>2016 IEEE Asian Hardware-Oriented Security and Trust >Inner collisions in ECC: Vulnerabilities of complete addition formulas for NIST curves
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Inner collisions in ECC: Vulnerabilities of complete addition formulas for NIST curves

机译：ECC中的内部冲突：NIST曲线的完整加法公式的漏洞

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摘要

Elliptic curve cryptosystems are built on an underlying additive group, with an addition operation defined as the group operation. The aim of the elliptic curve addition operation is to render an elliptic curve point on the underlying elliptic curve when two ECC points are taken as inputs. However ECC addition formula may not be complete in nature, and may contain exceptional points, for which the addition formula may fail to produce a valid third point. The addition formula for prime order NIST curves were in fact not complete, till Renes et. al. proposed a complete addition formula for the class of prime order NIST curves in their Eurocrypt 2016 paper. The property of completeness ensures a valid third ECC point for any two chosen input points, and thus provides the advantage of using the same formula for both addition and doubling operations. Consequently it is assumed to be inherently side-channel secure, however any practical validation against side-channel protection is not yet present in the literature. In this work we analyse the side-channel protection for this newly constructed unified formula against two horizontal attacks. We show although this new construction is resistant against HCCA, it may be vulnerable to the ROSETTA attack, which exploits inner collisions within field multiplication operations.
机译：椭圆曲线密码系统建立在基础加性组上，加法运算定义为组运算。椭圆曲线加法运算的目的是当将两个ECC点作为输入时，在基础椭圆曲线上绘制一个椭圆曲线点。但是，ECC加法公式本质上可能并不完整，并且可能包含例外点，为此，加法公式可能无法产生有效的第三点。实际上，直到Renes等人之前，素数NIST曲线的加法公式还不完整。等在Eurocrypt 2016论文中为素数NIST曲线类别提出了一个完整的加法公式。完整性属性可确保为任意两个选定的输入点提供有效的第三个ECC点，因此具有在加法和加倍运算中使用相同公式的优点。因此，假定它本质上是侧通道安全的，但是在文献中还没有针对侧通道保护的任何实际验证。在这项工作中，我们分析了此新构建的统一公式针对两个水平攻击的侧信道保护。我们显示，尽管这种新结构可以抵抗HCCA，但它可能容易受到ROSETTA攻击的侵害，后者利用场乘法运算中的内部冲突。

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