• Kim, Young-Sik (Department of Information and Communication Engineering, Chosun University) ;
  • Yeom, Yongjin (Department of Mathematics, Kookmin University) ;
  • Choi, Hee Bong (The Attached Institute of ETRI)
  • Received : 2012.09.19
  • Published : 2013.07.01


Shannon entropy is one of the widely used randomness measures especially for cryptographic applications. However, the conventional entropy tests are less sensitive to the inter-bit dependency in random samples. In this paper, we propose new online randomness test schemes for true random number generators (TRNGs) based on the mutual information between consecutive ${\kappa}$-bit output blocks for testing of inter-bit dependency in random samples. By estimating the block entropies of distinct lengths at the same time, it is possible to measure the mutual information, which is closely related to the amount of the statistical dependency between two consecutive data blocks. In addition, we propose a new estimation method for entropies, which accumulates intermediate values of the number of frequencies. The proposed method can estimate entropy with less samples than Maurer-Coron type entropy test can. By numerical simulations, it is shown that the new proposed scheme can be used as a reliable online entropy estimator for TRNGs used by cryptographic modules.


online test;TRNG;random number generation;statistical test;Shannon entropy;mutual information


Supported by : National Security Research Institute (NSRI)


  1. M. Bucci and R. Luzzi, Design of Testable Random Bit Generators, in Proc. CHES 2005, LNCS, vol. 3659, pp. 147-156, 2005.
  2. J.-S. Coron, On the security of random sources, in Proc. PKC'99, LNCS, vol. 1560, pp. 29-42, 1999.
  3. J.-S. Coron, An accurate evaluation of Maurer's universal test, Selected areas in cryptogra-phy (Kingston, ON, 1998), 57-71, Lecture Notes in Comput. Sci., 1556, Springer, Berlin, 1999.
  4. T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley & Sons, Inc., New York, 1991.
  5. W. Killmann and W. Schindler, A proposal for: functionality classes and evaluation methodology for true (physical) random number generators, AIS.31 Version 3.1, Sep. 25, 2001.
  6. U. M. Maurer, A universal statistical test for random bit generators, J. Cryptology 5 (1992), no. 2, 89-105.
  7. W. Schindler, Efficient online tests for true random number generators, in IACR Work-shop on Cryptographic Hardware and Embedded Systems, CHES 2001, LNCS., vol. 2162, pp. 103-117, Springer, Berlin, 2001.
  8. B. Sunar, W. Martin, and D. Stinson, A provably secure true random number generator with built-in tolerance to active attacks, IEEE Trans. Computers 56 (2007), no. 1, 109-119.
  9. E. Trichina, et al., Supplemental cryptographic hardware for smart cards, IEEE Micro. 21 (2001), no. 6, 26-35.
  10. I. Vasyltsov, et al., Fast digital TRNG based on metastable ring oscillator, in Proc. CHES 2008, LNCS, vol. 5154, pp. 164-180, 2008.