When cryptographical problems are treated in SAT solvers, they often contain large set of XOR constraints. Treating these XOR constraints through on-the-fly Gaussian elimination during solving has been shown to be a viable approach by Soos et al. [1]. We describe various enhancements to this scheme which increase the performance and mostly eliminate the need for manual tuning of parameters. With these enhancements, we were able achieve speedups of up to 29% on the Bivium and up to 45% on the

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... vium ciphers, contrary to the 1-5% speedup achieved by the original scheme.[1] Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In Kullmann, O., ed.: Theory and Applications of Satisfiability Testing — SAT 2009. Volume 5584 of Lecture Notes in Computer Science., Springer (2009) 244–257