ML-KEM (FIPS203) and ML-DSA (FIPS204) were two of the first post quantum cryptographyschemes to be standardized by the National Institute of Standards and Technology; Both CRYSTALSalgorithms utilize modulo reduction, specifically Montgomery reduction. Montgomery reduction tradition-ally is suited to computing moduli much larger than 32/64-bits and as such, the introduction of a newmodulo reduction method published by Thomas Plantard allows for more efficient modulo reduction thanMontgomery and Barrett as this new method allows for one less multiplication at the reduction stage. This isachieved by doubling the word size of the values being calculated, meaning the word size of data computedwithin CRYSTALS-Dilithium doubles from 32-bit to 64-bit and from 16-bit to 32-bit for CRYSTALS-Kyber.In this paper we present the worlds first Plantard ISEs ever that can compute both CRYSTALS-Kyber andCRYSTALS-Dilithium. Utilizing Plantard reduction as a set of Instruction Set Extensions, we are able toreduce the cycle counts required to compute the entire CRYSTALS-Kyber algorithm by up to 19.5% andreduce the cycle counts required to compute CRYSTALS-Dilithium by 26.6% as well as the CRYSTALS-Kyber INTT by 2.66× and the CRYSTALS-Dilithium INTT by 2.42×.
Bevin et al. (Thu,) studied this question.