Algebraic cryptanalysis of a small-scale version of stream cipher Lex

In this study, the authors analyse with respect to algebraic attacks a small-scale version of the stream cipher Lex. They base it on a small-scale version of the block cipher advanced encryption standard (AES) with 16-bit state and 16-bit key. They represent the small-scale Lex and its key schedule in two alternative ways: as a system of cubic boolean equations and as a system of quadratic boolean equations. The authors use Grobner bases to solve the two systems for different number of rounds and sizes of the leak. They obtain the best results for the quadratic representation of the cipher. For this case they are able to recover the secret key in time less than 2 min by solving a system of 374 quadratic boolean equations in 208 unknowns resulting from 5 rounds of the cipher.