176270
20180913061222.0
CONF
ElimLin Algorithm Revisited
2012
Springer
2012
Conference Papers
LNCS
ElimLin is a simple algorithm for solving polynomial systems of multivariate equations over small finite fields. It was initially proposed as a single tool by Courtois to attack DES. It can reveal some hidden linear equations existing in the ideal generated by the system. We report a number of key theorems on ElimLin. Our main result is to characterize ElimLin in terms of a sequence of intersections of vector spaces. It implies that the linear space generated by ElimLin is invariant with respect to any variable ordering during elimination and substitution. This can be seen as surprising given the fact that it eliminates variables. On the contrary, monomial ordering is a crucial factor in Grobner basis algorithms such as F4. Moreover, we prove that the result of ElimLin is invariant with respect to any affine bijective variable change. Analyzing an overdefined dense system of equations, we argue that to obtain more linear equations in the succeeding iteration in ElimLin some restrictions should be satisfied. Finally, we compare the security of LBlock and MIBS block ciphers with respect to algebraic attacks and propose several attacks on Courtois Toy Cipher version 2 (CTC2) with distinct parameters using ElimLin.
block ciphers
algebraic cryptanalysis
systems of sparse polynomial equations of low degree
Courtois, Nicolas
Sepehrdad, Pouyan
186617
243334
Susil, Petr
190647
244132
Vaudenay, Serge
131602
241950
FSE
Washington DC, USA
March 19-21, 2012
Proceedings of Fast Software Encryption
n/a
409193
n/a
http://infoscience.epfl.ch/record/176270/files/ElimLin_full_version.pdf
LASEC
252183
U10433
oai:infoscience.tind.io:176270
IC
conf
186617
EPFL-CONF-176270
EPFL
PUBLISHED
REVIEWED
CONF