Abstract
A new approach to synthesize bent Boolean functions by means of Cartesian Genetic Programming (CGP) has been proposed recently. Bent functions have important applications in cryptography due to their high nonlinearity. However, they are very rare and their discovery using conventional brute force methods is not efficient enough. In this paper, a new parallel implementation is proposed and the performance is evaluated on the Intel Xeon Phi Coprocessor.
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Miller, J.F., Thomson, P.: Cartesian Genetic Programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 121–132. Springer, Heidelberg (2000)
Hrbacek, R., Sekanina, L.: Towards highly optimized cartesian genetic programming: From sequential via simd and thread to massive parallel implementation. In: GECCO 2014 Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, Association for Computing Machinery, pp. 1015–1022 (2014)
Vasicek, Z., Sekanina, L.: On area minimization of complex combinational circuits using cartesian genetic programming. In: IEEE World Congress on Computational Intelligence. Institute of Electrical and Electronics Engineers 2012, pp. 2379–2386 (2012)
Vasicek, Z., Bidlo, M.: Evolutionary design of robust noise-specific image filters. In: IEEE Congress on Evolutionary Omputation, pp. 269–276. IEEE Computer Society (2011)
Hrbacek, R., Sikulova, M.: Coevolutionary cartesian genetic programming in fpga. In: Advances in Artificial Life, ECAL 2013, Proceedings of the Twelfth European Conference on the Synthesis and Simulation of Living Systems, pp. 431–438. MIT Press (2013)
Khan, G., Miller, J.: The cgp developmental network. In: Miller, J.F. (ed.) Cartesian Genetic Programming. Natural Computing Series, pp. 255–291. Springer, Berlin (2011)
Hrbacek, R., Dvorak, V.: Bent Function Synthesis by Means of Cartesian Genetic Programming. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 414–423. Springer, Heidelberg (2014)
Dobbertin, H.: Construction of bent functions and balanced boolean functions with high nonlinearity. In: Preneel, B. (ed.) Fast Software Encryption. LNCS, vol. 1008, pp. 61–74. Springer, Heidelberg (1995)
Butler, J.T., Sasao, T.: Logic functions for cryptography - a tutorial. In: Proceedings of the Reed-Muller Workshop (2009)
Shafer, J.L., Schneider, S.W., Butler, J.T., Stanica, P.: Enumeration of bent boolean functions by reconfigurable computer. In: Sass, R., Tessier, R. (eds.) FCCM, pp. 265–272. IEEE Computer Society (2010)
Rothaus, O.: On “ben” functions. Journal of Combinatorial Theory, Series A 20, 300–305 (1976)
Schneider, S.W.: Finding bent functions using genetic algorithms. Master’s thesis, Naval Postgraduate School, Monterey (2009)
Miller, J.F. (ed.): Cartesian Genetic Programming. Natural Computing Series. Springer (2011)
Hennessy, J., Patterson, D.: Computer Architecture: A Quantitative Approach. Elsevier Science, The Morgan Kaufmann Series in Computer Architecture and Design (2011)
Jeffers, J., Reinders, J.: Intel Xeon Phi coprocessor high-performance programming. Elsevier Waltham (Mass.), Amsterdam, Boston (Mass.), Heidelberg..., et al. (2013)
Warren, H.S.: Hacker’s Delight. 2nd edn. Addison-Wesley Professional (2012)
Intel: Intel xeon phi product family performance (2013). http://www.intel.com/content/www/us/en/benchmarks/xeon-phi-product-family-performance-brief.html
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Hrbacek, R. (2014). Bent Functions Synthesis on Intel Xeon Phi Coprocessor. In: Hliněný, P., et al. Mathematical and Engineering Methods in Computer Science. MEMICS 2014. Lecture Notes in Computer Science(), vol 8934. Springer, Cham. https://doi.org/10.1007/978-3-319-14896-0_8
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DOI: https://doi.org/10.1007/978-3-319-14896-0_8
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