Recently, Alkim, Ducas, Pöppelmann, and Schwabe proposed a Ring-LWE-based key exchange protocol called NewHope [2] and illustrated that this protocol is very ecient on large Intel processors. Their paper also claims that the parameter choice enables ecient implementation on small embedded processors. In this paper we show that these claims are actually correct and present NewHope software for the ARM Cortex-M family of 32-bit microcontrollers. More specically, our software targets the low-end Cortex-M0 and the high-end Cortex-M4 processor from this family. Our software starts from the C reference implementation by the designers of NewHope and then carefully optimizes subroutines in assembly. In particular, compared to best results known so far, our NTT implementation achieves a speedup of almost a factor of 2 on the Cortex-M4. Our Cortex-M0 NTT software slightly outperforms previously best results on the Cortex-M4, a much more powerful processor. In total, the server side of the key exchange executes in only 1 467 101 cycles on the M0 and only 860388 cycles on the M4; the client side executes in 1 738 922 cycles on the M0 and 984 761 cycles on the M4.

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This paper proposes various optimizations for lattice-based key encapsulation mechanisms (KEM) using the Number Theoretic Transform (NTT) on the popular ARM Cortex-M4 microcontroller. Improvements come in the form of a faster code using more efficient modular reductions, optimized small-degree polynomial multiplications, and more aggressive layer merging in the NTT, but also in the form of reduced stack usage. We test our optimizations in software implementations of Kyber and NewHope, both round 2 candidates in the NIST post-quantum project, and also NewHope-Compact, a recently proposed variant of NewHope with smaller parameters. Our software is the first implementation of NewHope-Compact on the Cortex-M4 and shows speed improvements over previous high-speed implementations of Kyber and NewHope. Moreover, it gives a common framework to compare those schemes with the same level of optimization. Our results show that NewHope- Compact is the fastest scheme, followed by Kyber, and finally NewHope, which seems to suffer from its large modulus and error distribution for small dimensions.

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