### Abstract

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 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.
Keywords: Elliptic-curve cryptography, verifiably random curves, verifiably pseudorandom curves, nothing- up-my-sleeve numbers, sabotaging standards, fighting terrorism, protecting the children

Original language | English |
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Publisher | IACR |

Number of pages | 18 |

Publication status | Published - 2014 |

### Publication series

Name | Cryptology ePrint Archive |
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Volume | 2014/571 |

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## Cite this

Bernstein, D. J., Chou, T., Chuengsatiansup, C., Hülsing, A. T., Lange, T., Niederhagen, R. F., & Vredendaal, van, C. (2014).

*How to manipulate curve standards : a white paper for the black hat*. (Cryptology ePrint Archive; Vol. 2014/571). IACR.