Abstract
Since its first introduction by Bellcore researchers, fault injection has been considered as a powerful and practical way to attack cryptosystems, especially when they are implemented on embedded devices. In this chapter, we will review how fault injection has been practically and efficiently exploited to attack some implementations of the celebrated RSA. The first attacks were based on perturbing execution flow or a private key; powerful attacks exploiting modifications in the public key have recently appeared. These new attacks are particularly relevant since they highlights the need for also protecting public key elements against faults.
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Notes
- 1.
\(p\) is a prime number such that \(p \lnot \mid \dot{m_i}\) and \(p \lnot \mid S_i\).
- 2.
When \(e\) is small, the authors take advantage of the RSA equation \(e \cdot d \equiv 1 \mathrm{ mod}{\varphi (N)}\) to determine the most significant part of \(d\). Indeed, knowing that \(\varphi (N) = N + 1 - p - q \approx N\) for its most significant part, then \(d \approx \frac{1 + k \cdot (N+1)}{e}\) with \(k < e\). Hence, if \(e\) is small (e.g. \(e = 2^16+1\)), the most significant part of \(d\) can be directly deduced from the previous relation completed by an exhaustive search on \(k\).
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© 2012 Springer-Verlag Berlin Heidelberg
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Berzati, A., Canovas-Dumas, C., Goubin, L. (2012). A Survey of Differential Fault Analysis Against Classical RSA Implementations. In: Joye, M., Tunstall, M. (eds) Fault Analysis in Cryptography. Information Security and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29656-7_7
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DOI: https://doi.org/10.1007/978-3-642-29656-7_7
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