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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Fault Attacks on Projective-to-Affine Coordinates Conversion
verfasst von : Diana Maimuţ, Cédric Murdica, David Naccache, Mehdi Tibouchi
Erschienen in: Constructive Side-Channel Analysis and Secure Design
Verlag: Springer Berlin Heidelberg
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This paper presents a new type of fault attacks on elliptic curves cryptosystems.
At EUROCRYPT 2004, Naccache
et alii
showed that when the result of an elliptic curve scalar multiplication [
k
]
P
(computed using a fixed scalar multiplication algorithm, such as double-and-add) is given in projective coordinates, an attacker can recover information on
k
. The attack is somewhat theoretical, because elliptic curve cryptosystems implementations usually convert scalar multiplication’s result back to affine coordinates before outputting [
k
]
P
.
This paper explains how injecting faults in the final projective-to-affine coordinate conversion enables an attacker to retrieve the projective coordinates of [
k
]
P
, making Naccache
et alii
’s attack also applicable to implementations that output points in affine coordinates. As a result, such faults allow the recovery of information about
k
.