Abstract
Statistical tests have been applied to measures obtained from partitioning the keystream of a stream cipher into subsets of a given length. Similarly, the strength of a block cipher has been measured by applying statistical tests to subsets obtained from both the input and output blocks. There are problems in applying these tests as the size of the subsets increases. We propose a novel method based on the classical occupancy problem to deal with larger subsets in testing for randomness in a keystream in the case of a stream cipher and for independence between subsets of input and output blocks in the case of a block cipher.
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References
H. Beker and F. Piper Cipher Systems: The Protection of Communications, Wiley, 1982.
W. Caelli, E. Dawson, H. Gustafson and L. Nielsen CRYPT-X Package, Office of Commercial Services, Queensland University of Technology, Australia, 1992. ISBN 0 86856 8090.
J. Carroll and L. Robins, Computer Cryptanalysis, Technical Report No. 223, 1988, Deptartment of Computer Science, The University of Western Ontario, London, Ontario.
W. Feller, An Introduction to Probability Theory and Its Applications, 1, 2nd edition, Wiley, 1968.
L. J. Folks, Combination of Independent Tests, Handbook of Statistics, 4, Elsevier, 1984, 113–121.
J. Dj. Golić, On the Security of Shift Register Based Keystream Generators, Fast Software Encryption '93, Lecture Notes in Computer Science, 803, R. J. Anderson ed., Springer-Verlag, 1994, 90–100.
N. L. Johnson and S. Kotz, Urn Models and Their Application, Wiley, 1977.
D. Knuth, The Art of Computer Programming: Seminumerical Algorithms, 2, Addison Wesley, 1973.
D. Knuth, The Art of Computer Programming: Sorting and Searching, 3, Addison Wesley, 1973.
V. F. Kolchin, The Speed of Convergence to Limit Distributions in the Classical Ball Problem, Theory of Probability and its Applications, 11, 1966, 128–140.
A. G. Konheim, Cryptography — A Primer, Wiley, New York, 1981.
A. Lempel and J. Ziv, On the Complexity of Finite Sequences, IEEE Transactions on Information Theory, IT-22, 1976, 75–81.
J. L. Massey, Shift Register Synthesis and BCH Decoding, IEEE Transactions on Information Theory, IT-15, 1969, 122–127.
U. M. Maurer, A Universal Statistical Test for Random Bit Generators, Journal of Cryptology, 5, 1992, 89–105.
C. H. Meyer and S. M. Matyas, Cryptography — A New Dimension in Data Security, John Wiley & Sons, New York, 1982.
A. N. Pettitt, A Non-parametric Approach to the Change-point Problem, Applied Statistics, 28, No. 2, 1979, 126–135.
R. A. Rueppel Analysis and Design of Stream Ciphers, Springer-Verlag, 1986.
R. A. Rueppel, Stream Ciphers, Contemporary Cryptology: The Science of Information Integrity, G. J. Simmons ed., IEEE Press, New York, 1992, 65–134.
C. E. Shannon, Communication Theory of Secrecy Systems, Bell System Technical Journal, 28, 1949, 656–715.
A. Shimizu and S. Miyaguchi, FEAL — Fast Data Encryption Algorithm, Systems and Computers in Japan, 19, No. 7, 1988, 20–34.
M. A. Stephens and R. B. D'Agostino, Tests Based on EDF Statistics, Goodness of Fit Techniques, Statistics, Textbooks and Monographs, 68, Marcel Dekker Inc., 1986, 97–193.
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© 1996 Springer-Verlag Berlin Heidelberg
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Gustafson, H.M., Dawson, E.P., Golić, J.D. (1996). Randomness measures related to subset occurrence. In: Dawson, E., Golić, J. (eds) Cryptography: Policy and Algorithms. CPA 1995. Lecture Notes in Computer Science, vol 1029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032353
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DOI: https://doi.org/10.1007/BFb0032353
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