We present implementations of the lattice-based digital signature scheme Dilithium for ARM Cortex-M3 and ARM Cortex-M4. Dilithium is one of the three signature finalists of the NIST post-quantum cryptography competition. As our Cortex-M4 target, we use the popular STM32F407-DISCOVERY development board. Compared to the previous speed records on the Cortex-M4 by Ravi, Gupta, Chattopadhyay, and Bhasin we speed up the key operations NTT and NTT−1 by 20% which together with other optimizations results in speedups of 7%, 15%, and 9% for Dilithium3 key generation, signing, and verification respectively. We also present the first constant-time Dilithium implementation on the Cortex-M3 and use the Arduino Due for benchmarks. For Dilithium3, we achieve on average 2 562 kilocycles for key generation, 10 667 kilocycles for signing, and 2 321 kilocycles for verification.Additionally, we present stack consumption optimizations applying to both our Cortex- M3 and Cortex-M4 implementation. Due to the iterative nature of the Dilithium signing algorithm, there is no optimal way to achieve the best speed and lowest stack consumption at the same time. We present three different strategies for the signing procedure which allow trading more stack and flash memory for faster speed or viceversa. Our implementation of Dilithium3 with the smallest memory footprint uses less than 12kB. As an additional output of this work, we present the first Cortex-M3 implementations of the key-encapsulation schemes NewHope and Kyber.

This paper presents faster implementations of the latticebased schemes Dilithium and Kyber on the Cortex-M4. Dilithium is one of three signature finalists in the NIST post-quantum project (NIST PQC), while Kyber is one of four key-encapsulation mechanism (KEM) finalists.Our optimizations affect the core polynomial arithmetic involving number-theoretic transforms in both schemes. Our main contributions are threefold: We present a faster signed Barrett reduction for Kyber, propose to switch to a smaller prime modulus for the polynomial multiplications cs1 and cs2 in the signing procedure of Dilithium, and apply various known optimizations to the polynomial arithmetic in both schemes. Using a smaller prime modulus is particularly interesting as it allows using the Fermat number transform resulting in especially fast code.We outperform the state-of-the-art for both Dilithium and Kyber. For Dilithium, our NTT and iNTT are faster by 5.2% and 5.7%. Switching to a smaller modulus results in speed-up of 33.1%-37.6% for the relevant operations (sum of the base multiplication and iNTT) in the signing procedure. For Kyber, the optimizations results in 15.9%-17.8% faster matrix-vector product which is a core arithmetic operation in Kyber.

A major challenge when applying cryptography on constrained environments is the trade-off between performance and security. In this work, we analyzed different strategies for the optimization of several candidates of NIST's lightweight cryptography standardization project on a RISC-V architecture. In particular, we studied the general impact of optimizing symmetric-key algorithms in assembly and in plain C. Furthermore, we present optimized implementations, achieving a speed-up of up to 81% over available implementations, and discuss general implementation strategies.

This paper presents optimized software for constant-time variable-base scalar multiplication on prime-order Weierstraß curves using the complete addition and doubling formulas presented by Renes, Costello, and Batina in 2016. Our software targets three different microarchitectures: Intel Sandy Bridge, Intel Haswell, and ARM Cortex-M4. We use a 255-bit elliptic curve over F 2 255 −19 that was proposed by Barreto in 2017. The reason for choosing this curve in our software is that it allows most meaningful comparison of our results with optimized software for Curve25519. The goal of this comparison is to get an understanding of the cost of using cofactor-one curves with complete formulas when compared to widely used Montgomery (or twisted Edwards) curves that inherently have a non-trivial cofactor.