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Inner Collisions in ECC: Vulnerabilities of Complete Addition Formulas for NIST curves

机译:ECC中的内部碰撞:NIST曲线的完整添加公式的漏洞

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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:椭圆曲线密码系统基于底层添加剂组,具有作为组操作的加法操作。椭圆曲线加法操作的目的是在将两个ECC点作为输入中呈现底层椭圆曲线上的椭圆曲线点。然而,ECC添加公式可能无法完整,并且可能包含异常点,因此添加公式可能无法产生有效的第三点。 Prime Order NIST曲线的加值公式实际上没有完成,直到renes等。 al。为他们的Eurocrypt 2016纸张中提出了一个完整的加法公式,以获取欧元兑欧元兑金纸中的主要订单NIST曲线。完整性的属性可确保任何两个所选择的输入点的有效第三ECC点,从而提供了使用相同的公式来添加和加倍操作的优点。因此,假设具有固有的侧通道安全,但是对文献中尚未存在对侧通道保护的任何实际验证。在这项工作中,我们分析了这种新构建的统一公式的侧通道保护,免于两个水平攻击。我们展示了这种新的建筑对HCCA抵抗,可能很容易受到Rosetta攻击的影响,这是利用现场乘法操作内的内部冲突。

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