Abstract
Random number generators (RNGs) play an important role in many real-world applications. Besides true hardware RNGs, one important class are deterministic random number generators. Such generators do not possess the unpredictability of true RNGs, but still have a widespread usage. For a deterministic RNG to be used in cryptography, it needs to fulfill a number of conditions related to the speed, the security, and the ease of implementation. In this paper, we investigate how to evolve deterministic RNGs with Cartesian Genetic Programming. Our results show that such evolved generators easily pass all randomness tests and are extremely fast/small in hardware.
Keywords
- Random number generators
- Pseudorandomness
- Cryptography
- Cartesian Genetic Programming
- Statistical tests
This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-4882. In addition, this work was supported in part by the Research Council KU Leuven (C16/15/058) and IOF project EDA-DSE (HB/13/020).
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References
Katz, J., Lindell, Y.: Introduction to Modern Cryptography, 2nd edn. Chapman and Hall/CRC, Boca Raton (2014)
Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo random number generator. SIAM J. Comput. 15(2), 364–383 (1986)
Danger, J.L., Guilley, S., Barthe, L., Benoit, P.: Countermeasures against physical attacks in FPGAs. In: Badrignans, B., Danger, L.J., Fischer, V., Gogniat, G., Torres, L. (eds.) Security Trends for FPGAS: From Secured to Secure Reconfigurable Systems, pp. 73–100. Springer, Dordrecht (2011)
Lamenca-Martinez, C., Hernandez-Castro, J.C., Estevez-Tapiador, J.M., Ribagorda, A.: Lamar: a new pseudorandom number generator evolved by means of genetic programming. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 850–859. Springer, Heidelberg (2006)
Peris-Lopez, P., Hernandez-Castro, J.C., Estevez-Tapiador, J.M., Ribagorda, A.: LAMED - a PRNG for EPC class-1 generation-2 RFID specification. Comput. Stand. Interfaces 31(1), 88–97 (2009)
Killmann, W., Schindler, W.: A proposal for: functionality classes for random number generators. Bundesamt für Sicherheit in der Informationstechnik (BSI), Germany (2011)
Bassham, III, Lawrence, E., Rukhin, A.L., Soto, J., Nechvatal, J.R., Smid, M.E., Barker, E.B., Leigh, S.D., Levenson, M., Vangel, M., Banks, D.L., Heckert, N.A., Dray, J.F., Vo, S.: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, SP 800-22 Rev. 1a. National Institute of Standards & Technology, Gaithersburg, MD, USA (2010)
Marsaglia, G.: The Marsaglia Random Number CDROM including the Diehard Battery of Tests of Randomness (1995). http://www.stat.fsu.edu/pub/diehard/
Koza, J.R.: Evolving a computer program to generate random numbers using the genetic programming paradigm. In: Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 37–44. Morgan Kaufmann (1991)
Hernandez, J., Seznec, A., Isasi, P.: On the design of state-of-the-art pseudorandom number generators by means of genetic programming. In: Congress on Evolutionary Computation, CEC2004, vol. 2, pp. 1510–1516, June 2004
Warren, H.S.: Hacker’s Delight. Addison-Wesley Longman Publishing Co., Inc., Boston (2002)
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)
Tian, X., Benkrid, K.: Mersenne twister random number generation on FPGA, CPU and GPU. In: NASA/ESA Conference on Adaptive Hardware and Systems, AHS 2009, pp. 460–464, July 2009
Picek, S., Jakobovic, D., Miller, J.F., Batina, L., Cupic, M.: Cryptographic boolean functions: one output, many design criteria. Appl. Soft Comput. 40, 635–653 (2016)
Sekanina, L.: Virtual reconfigurable circuits for real-world applications of evolvable hardware. In: Tyrrell, A.M., Haddow, P.C., Torresen, J. (eds.) ICES 2003. LNCS, vol. 2606, pp. 186–197. Springer, Heidelberg (2003)
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Picek, S., Sisejkovic, D., Rozic, V., Yang, B., Jakobovic, D., Mentens, N. (2016). Evolving Cryptographic Pseudorandom Number Generators. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_57
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DOI: https://doi.org/10.1007/978-3-319-45823-6_57
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