Abstract
We address the question of how a computationally limited device may outsource pairing computation in cryptography to another, potentially malicious, but much more computationally powerful device. We introduce two new efficient protocols for securely outsourcing pairing computations to an untrusted helper. The first generic scheme is proven computationally secure (and can be proven statistically secure at the expense of worse performance). It allows various communication-efficiency trade-offs. The second specific scheme – for optimal Ate pairing on a Barreto-Naehrig curve – is unconditionally secure, and do not rely on any hardness assumptions. Both protocols are more efficient than the actual computation of the pairing by the restricted device and in particular they are more efficient than all previous proposals.
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Notes
- 1.
It is worth mentioning that this computational cost can be further decreased by using classical multi-exponentiation techniques (in particular for small values of \(n\) (e.g. \(n = 5\)).
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Acknowledgements
The authors thank Olivier Blazy, Renaud Dubois and Fabien Laguillaumie for their fruitful comments. This work was supported in part by the French ANR-12-INSE-0014 SIMPATIC Project.
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Guillevic, A., Vergnaud, D. (2015). Algorithms for Outsourcing Pairing Computation. In: Joye, M., Moradi, A. (eds) Smart Card Research and Advanced Applications. CARDIS 2014. Lecture Notes in Computer Science(), vol 8968. Springer, Cham. https://doi.org/10.1007/978-3-319-16763-3_12
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