Abstract
In 2017, NIST shook the cryptographic world by starting a process for standardizing post-quantum cryptography. Sixty-four submissions have been considered for the first round of the on-going NIST Post-Quantum Cryptography (PQC) process. Multivariate cryptography is a classical post-quantum candidate that turns to be the most represented in the signature category. At this stage of the process, it is of primary importance to investigate efficient implementations of the candidates. This article presents MQsoft, an efficient library which permits to implement HFE-based multivariate schemes submitted to the NIST PQC process such as GeMSS, Gui and DualModeMS. The library is implemented in C targeting Intel 64-bit processors and using avx2 set instructions. We present performance results for our library and its application to GeMSS, Gui and DualModeMS. In particular, we optimize several crucial parts for these schemes. These include root finding for HFE polynomials and evaluation of multivariate quadratic systems in F2. We propose a new method which accelerates root finding for specific HFE polynomials by a factor of two. For GeMSS and Gui, we obtain a speed-up of a factor between 2 and 19 for the keypair generation, between 1.2 and 2.5 for the signature generation, and between 1.6 and 2 for the verifying process. We have also improved the arithmetic in F2n by a factor of 4 compared to the NTL library. Moreover, a large part of our implementation is protected against timing attacks.
Highlights
The recent progress on the development of quantum computers has motivated NIST [oST17] to start a standardization process for post-quantum cryptography
Our software tools allow to speed-up the GeMSS [CFMR+17], Gui [CDP+17] and DualModeMS [FPR17] signature schemes, which are candidates submitted to the NIST post-quantum cryptography standardization process [oST17]
Since the multivariate quadratic systems will be evaluated in Fn2+v, x2i = xi and so, the linear term xi is stored with the term x2i of
Summary
The recent progress on the development of quantum computers has motivated NIST [oST17] to start a standardization process for post-quantum cryptography. The choice of the best candidate is based on its security and its performance. At this stage, the security parameters of the candidates are already fixed, but the implementations can be improved. We study the efficient implementation of multivariate schemes. We present here software tools that allow the efficient implementation of HFE-based schemes (using arithmetic in F2n ). Our software tools allow to speed-up the GeMSS [CFMR+17], Gui [CDP+17] and DualModeMS [FPR17] signature schemes, which are candidates submitted to the NIST post-quantum cryptography standardization process [oST17]. IACR Transactions on Cryptographic Hardware and Embedded Systems ISSN 2569-2925, Vol 2019, No 3, pp. 257–304 DOI:10.13154/tches.v2019.i3.257-304
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