Abstract
Dilithium is a round 2 candidate for digital signature schemes in NIST initiative for post-quantum cryptographic schemes. Since Dilithium is built upon the “Fiat Shamir with Aborts” framework, its signing procedure performs rejection sampling of its signatures to ensure they do not leak information about the secret key. Thus, the signing procedure is iterative in nature with a number of rejected iterations, which serve as unnecessary overheads hampering its overall performance. As a first contribution, we propose an optimization that reduces the computations in the rejected iterations through early-evaluation of the conditional checks. This allows to perform an early detection of the rejection condition and reject a given iteration as early as possible. We also incorporate a number of standard optimizations such as unrolling and inlining to further improve the speed of the signing procedure. We incorporate and evaluate our optimizations over the software implementation of Dilithium on both the Intel Core i5-4460 and ARM Cortex-M4 CPUs. As a second contribution, we identify opportunities to present a more refined evaluation of Dilithium’s signing procedure in several scenarios where pre-computations can be carried out. We also evaluate the performance of our optimizations and the memory requirements for the pre-computed intermediates in the considered scenarios. We could yield speed-ups in the range of 6% upto 35%, considering all the aforementioned scenarios, thus presenting the fastest software implementation of Dilithium till date.
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Notes
- 1.
The code snippet shown in Fig. 1 is in its static single assignment form. In the static single assignment code, the result of an operation is always written to a new variable. In the original implementation, all of \(\mathbf {z}_i\) for \(i = \{0,\ldots ,3\}\) refer to a single variable \(\mathbf {z}\). The single assignment form is used for better illustration of our idea.
- 2.
The authors of Dilithium also note that the above operations can be pre-computed and stored to “slightly” speed up the signing operation, but do not present any performance evaluation or the memory requirements due to the same (Refer Sec. 3.1 of [8]).
- 3.
By precomputed iterations, we do not mean computation of the complete iterations, but only computation of \(\mathbf {y}, \mathbf {w}_0\) and \(\mathbf {w}_1\) corresponding to those iterations.
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Acknowledgment
The authors acknowledge the support from the Singapore National Research Foundation (“SOCure” grant NRF2018NCR-NCR002-0001 – www.green-ic.org/socure). This work is also partially supported by NRF TUM CREATE grant.
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Ravi, P., Gupta, S.S., Chattopadhyay, A., Bhasin, S. (2020). Improving Speed of Dilithium’s Signing Procedure. In: Belaïd, S., Güneysu, T. (eds) Smart Card Research and Advanced Applications. CARDIS 2019. Lecture Notes in Computer Science(), vol 11833. Springer, Cham. https://doi.org/10.1007/978-3-030-42068-0_4
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