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Elliptic Curve Cryptosystems in the Presence of Permanent and Transient Faults

机译:存在永久性和暂时性故障的椭圆曲线密码系统

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摘要

Elliptic curve cryptosystems in the presence of faults were studied by [Biehl et al., Advances in Cryptology - CRYPTO 2000, Springer Verlag (2000) pp. 131-146]. The first fault model they consider requires that the input point P in the computation of dP is chosen by the adversary. Their second and third fault models only require the knowledge of P. But these two latter models are less 'practical' in the sense that they assume that only a few bits of error are inserted (typically exactly one bit is supposed to be disturbed) either into P just prior to the point multiplication or during the course of the computation in a chosen location. This paper relaxes these assumptions and shows how random (and thus unknown) errors in either coordinates of point P, in the elliptic curve parameters or in the field representation enable the (partial) recovery of multiplier d. Then, from multiple point multiplications, we explain how this can be turned into a total key recovery. Simple precautions to prevent the leakage of secrets are also discussed.
机译:[Biehl et al。,Advances in Cryptology-CRYPTO 2000,Springer Verlag(2000)pp。131-146]研究了存在故障的椭圆曲线密码系统。他们考虑的第一个故障模型要求dP计算中的输入点P由对手选择。他们的第二个和第三个故障模型只需要P的知识。但是,后两个模型在假定仅插入少量错误(通常只干扰一个比特)的意义上就不太“实用”。恰好在点乘法之前或在选定位置的计算过程中将其存入P。本文放宽了这些假设,并说明了点P的坐标,椭圆曲线参数或场表示中的随机(因而未知)误差如何使乘数d(部分)恢复。然后,通过多点乘法,我们解释了如何将其转换为总密钥恢复。还讨论了防止机密泄漏的简单预防措施。

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