Abstract
In contrast to classical signature schemes, such as RSA or ECDSA signatures, the lattice-based signature scheme ring-TESLA is expected to be resistant even against quantum adversaries. Due to a recent key recovery from a lattice-based implementation, it becomes clear that cache side channels are a serious threat for lattice-based implementations. In this article, we analyze an existing implementation of ring-TESLA against cache side channels. To reduce the effort for manual code inspection, we selectively employ automated program analysis. The leakage bounds we compute with program analysis are sound overapproximations of cache-side-channel leakage. We detect four cache-side-channel vulnerabilities in the implementation of ring-TESLA. Since two vulnerabilities occur in implementations of techniques common to lattice-based schemes, they are also interesting beyond ring-TESLA. Finally, we show how the detected vulnerabilities can be mitigated effectively.
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Notes
- 1.
We analyze an implementation of ring-TESLA despite an error that was detected in its security reduction, since we expect that reductions given for its predecessor TESLA [14, 15] will be applicable to ring-TESLA as well. Hence, we consider it to be a good candidate for practical applications that require post-quantum signatures.
- 2.
Security properties of schemes over standard lattices (like TESLA) often hold for corresponding schemes over ideal lattices (like ring-TESLA), e.g., the security reduction from [11] holds for the standard-lattice variant and for the ideal-lattice variant.
- 3.
The instructions 0xF7/3 and 0x99 were integrated independently but concurrently into a different version of CacheAudit by Doychev [27].
- 4.
We also investigated FIFO (first in first out) replacement. The leakage bounds (on the unmitigated implementation) are less than 10 bit lower than under LRU.
- 5.
Treating the message as secret is overly conservative in a signature scenario. We investigated the effect of fixing the message to all ‘0’s and obtained the same leakage bounds as for an uninitialized message in the unmitigated implementation.
- 6.
Throughout the article, we round bounds up to one decimal place and truncate the bounds to \(3*\text {PARAM\_N}*32\text {bit}=49152\text {bit}\), i.e., the maximum size of the key.
- 7.
The analysis of the other subroutines of
can be found in the corresponding technical report under http://eprint.iacr.org/2017/951. - 8.
To simplify our explanation we assume that the corresponding cache line starts with
and ends with 
. - 9.
Our arguments hold also true if we assume that
is not loaded in the cache. In the ring-TESLA implementation, it is already loaded in line 18 in Listing 3.1.
can be found in the corresponding technical report under 
and ends with 
.
is not loaded in the cache. In the ring-TESLA implementation, it is already loaded in line 18 in Listing 3.1.References
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Acknowledgements
We thank the anonymous reviewers for their helpful suggestions and Sedat Akleylek for contributing to our modifications of the original ring-TESLA implementation. This work has been partially funded by the DFG as part of projects P1 and E3 within the CRC 1119 CROSSING.
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Bindel, N., Buchmann, J., Krämer, J., Mantel, H., Schickel, J., Weber, A. (2018). Bounding the Cache-Side-Channel Leakage of Lattice-Based Signature Schemes Using Program Semantics. In: Imine, A., Fernandez, J., Marion, JY., Logrippo, L., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2017. Lecture Notes in Computer Science(), vol 10723. Springer, Cham. https://doi.org/10.1007/978-3-319-75650-9_15
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