  The "Gluing Algorithm" of Semaev [Des.\ Codes Cryptogr.\ 49 (2008), 47--60]
--- that finds all solutions of a sparse system of linear equations over the
Galois field $GF(q)$ --- has average running time $O(mq^{\max \left\vert
\cup_{1}^{k}X_{j}\right\vert -k}), $ where $m$ is the total number of
equations, and $\cup_{1}^{k}X_{j}$ is the set of all unknowns actively
occurring in the first $k$ equations. Our goal here is to minimize the exponent
of $q$ in the case where every equation contains at most three unknowns.
%Applying hypergraph-theoretic methods we prove The main result states that if
the total number $\left\vert \cup_{1}^{m}X_{j}\right\vert$ of unknowns is equal
to $m$, then the best achievable exponent is between $c_1m$ and $c_2m$ for some
positive constants $c_1$ and $c_2.$

Cryptography and Security;Combinatorics