Synthesizing Shortest Linear Straight-Line Programs over GF(2) Using SAT
Non-trivial linear straight-line programs over the Galois field of two elements occur frequently in applications such as encryption or high-performance computing. Finding the shortest linear straight-line program for a given set of linear forms is known to be MaxSNP-complete, i.e., there is no ε-approximation for the problem unless P = NP.
This paper presents a non-approximative approach for finding the shortest linear straight-line program. In other words, we show how to search for a circuit of XOR gates with the minimal number of such gates. The approach is based on a reduction of the associated decision problem (“Is there a program of length k?”) to satisfiability of propositional logic. Using modern SAT solvers, optimal solutions to interesting problem instances can be obtained.
Unable to display preview. Download preview PDF.
- 3.Boyar, J., Peralta, R.: A new technique for combinational circuit optimization and a new circuit for the S-Box for AES. In: Patent Application Number 61089998 filed with the U.S. Patent and Trademark Office (2009)Google Scholar
- 4.Boyar, J., Peralta, R.: A new combinational logic minimization technique with applications to cryptology. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 178–189. Springer, Heidelberg (2010)Google Scholar
- 12.Le Berre, D., Parrain, A.: SAT4J, http://www.sat4j.org
- 13.Federal Information Processing Standard 197. The advanced encryption standard. Technical report, National Institute of Standards and Technology (2001)Google Scholar
- 14.Tseitin, G.: On the complexity of derivation in propositional calculus. Studies in Constructive Mathematics and Mathematical Logic, pp. 115–125 (1968); Reprinted in Automation of Reasoning 2, 466–483 (1983)Google Scholar