A Generalised Successive Resultants Algorithm

Davenport, James H.; Petit, Christophe; Pring, Benjamin

doi:10.1007/978-3-319-55227-9_9

Cited by 2 publications

(2 citation statements)

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“…In comparison to Berlekamp, SRA is interesting only when the polynomial has many roots. In [GvdHL15] and [DPP16], the root finding is improved for split and separable polynomials, and when the cardinality of multiplicative group is smooth. In our case, this method is not interesting because the HFE polynomials does not have many roots.…”

Section: Efficient Implementation Of Root Finding In F 2 N [X]mentioning

confidence: 99%

“…Recently, the successive resultants algorithm (SRA) [Pet14] has been proposed to find the roots of a polynomial in small characteristic, and this work has been extended for split polynomials in general finite fields. In [DPP16], root finding is improved for split and separable polynomials, when the cardinality of multiplicative group is smooth. In the case of the HFE polynomial F in F 2 n [X], F has a sparse structure and its coefficients are in a field of small characteristic.…”

Section: Introductionmentioning

confidence: 99%

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Software Toolkit for HFE-based Multivariate Schemes

Faugère¹,

Perret²,

Ryckeghem³

2019

TCHES

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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.

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Section: Efficient Implementation Of Root Finding In F 2 N [X]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%