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How to Manipulate Curve Standards: A White Paper for the Black Hat http://bada55.cr.yp.to

2015; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-319-27152-1_6

1611-3349

Daniel J. Bernstein, Tung Chou, Chitchanok Chuengsatiansup, Andreas Hülsing, Eran Lambooij, Tanja Lange, Ruben Niederhagen, Christine van Vredendaal,

Image Processing and 3D Reconstruction

This paper analyzes the cost of breaking ECC under the following assumptions: (1) ECC is using a standardized elliptic curve that was actually chosen by an attacker; (2) the attacker is aware of a vulnerability in some curves that are not publicly known to be vulnerable. This cost includes the cost of exploiting the vulnerability, but also the initial cost of computing a curve suitable for sabotaging the standard. This initial cost depends heavily upon the acceptability criteria used by the public to decide whether to allow a curve as a standard, and (in most cases) also upon the chance of a curve being vulnerable. This paper shows the importance of accurately modeling the actual acceptability criteria: i.e., figuring out what the public can be fooled into accepting. For example, this paper shows that plausible models of the “Brainpool acceptability criteria” allow the attacker to target a one-in-a-million vulnerability and that plausible models of the “Microsoft NUMS criteria” allow the attacker to target a one-in-a-hundred-thousand vulnerability.