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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.
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 19 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |