Cryptology ePrint Archive: Report 2019/1160

Cryptanalysis of the Multivariate Encryption Scheme EFLASH

Morten Øygarden and Patrick Felke and Håvard Raddum and Carlos Cid

Abstract: EFLASH is a multivariate public-key encryption scheme proposed by Cartor and Smith-Tone at SAC 2018. In this paper we investigate the hardness of solving the particular equation systems arising from EFLASH, and show that the solving degree for these types of systems is much lower than estimated by the authors. We show that a Gröbner basis algorithm will produce degree fall polynomials at a low degree for EFLASH systems. In particular we are able to accurately predict the number of these polynomials occurring at step degrees 3 and 4 in our attacks. We performed several experiments using the computer algebra system MAGMA, which indicate that the solving degree is at most one higher than the one where degree fall polynomials occur; moreover, our experiments show that whenever the predicted number of degree fall polynomials is positive, it is exact. Our conclusion is that EFLASH does not offer the level of security claimed by the designers. In particular, we estimate that the EFLASH version with 80-bit security parameters offers at most 69 bits of security.

Category / Keywords: public-key cryptography / multivariate cryptography, cryptanalysis, Gröbner basis

Date: received 6 Oct 2019

Contact author: carlos cid at rhul ac uk, morten oygarden at simula no, haavardr at simula no, patrick felke at hs-emden-leer de

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Version: 20191007:082605 (All versions of this report)

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