previous up next contents index
Previous: 1.9 En conclusion Up: Simulations Next: 2. Générateurs non uniformes   Contents   Index

Bibliography

1
Bach E. : "How to Generate Factored Random Numbers", SIAM Journal on Computing, Vol 17, No 2, pp. 179-192, apr. 1988.

2
Bays C. and S. Durham : "Improving Poor Random Number Generator", ACM Transaction on Mathematical Software, Vol 02, No 1, pp. 59-64, mar. 1976.

3
Ben-Or M. : "Probabilistic Algorithms In Finite Fields", IEEE Symposium on the Foundations of Computer Science, 22th SFCS, p394-398, 1981.

4
Blum M. and S. Micali : "How to Generate Cryptographically Strong Sequences of Pseudo-random Bits", SIAM J. on Computing, Vol 13, No 4, pp. 850-864, nov. 1984.

5
Blum L., M. Blum and M. Shub : "Simple Unpredictable Pseudo-random Number Generator", SIAM Journal on Computing, Vol 15, No 2, pp. 364-383, may. 1986.

6
Boyard J. : "Inferring Sequences Produced by Pseudo Random Number Generators", Journal of the ACM, Vol 36, No 1, pp. 129-141, jan. 1989.

7
Brown K.S. : "Periods of Fibonacci sequences mod m", available at http://www.seanet.com/ksbrown/kmath078.htm

8
Cheng R.C.H. : "Distribution fitting and random number and variate generation", Proc. of the 1992 WSC, pp. 74-81, 1992.

9
Chor B. and O. Goldreich : "Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity", SIAM J. on Computing, Vol 17, No 2, pp. 230-261, apr. 1988.

10
Collings B.J. and G.B. Hembree : "Initializing Generalized Feedback Shift Registers Pseudorandom Number Generators", Journal of the ACM, Vol 33, No 4, pp. 707-711, oct. 1986.

11
Compagner A. : "Fast and reliable random-number generation", Proc of the 1992 WSC, pp. 438-442, 1992.

12
Couture R. and P. L'Ecuyer : "Linear recurrences with carry as uniform random generators", Proc. of the 1995 WSC, pp. 263-267, 1995.

13
Couture R. and P. L'Ecuyer : "Distribution properties of multiply-with-carry random number generators", Mathematics of computation, Vol 66, No 218, pp. 591-607, 1997

14
Coveyou R.R. and R.D. Macpherson : "Fourier analysis of uniform random number generators", Journal of the ACM, Vol 14, No 1, pp. 100-119, jan. 1967.

15
Deng L.Y. and Y.C. Chu : "On improving pseudo-random number generators", Proc. of the 1991 WSC, pp. 1035-1042, 1991.

16
Dieter U. : "Statistical interdependence of pseudo-random numbers generated by the linear congruential method", pp. 287-317 in Applications of Number Theory to Numerical Analysis. Z. K. Zaremba, Ed., Academic Press, New York, 1972.

17
Durst M.J. : "Using linear congruential generators for parallel random number generation", Proc. of the 1989 WSC, pp.462-466, 1989.

18
Durstenfeld R. : "Algorithm 235, Random Permutations, Procedure Shuffle", Communications of the ACM, Vol 07, No 7, pp. 420, jul. 1964.

19
Etzion T. and A. Lempel : "Algorithm for the Generation of Full Length Shift Register Sequences", IEEE Transactions on Information Theory, Vol 30, No 3, pp. 480-484, may. 1984.

20
Fishman G.S. and L.R. Moore : "An exhaustive analysis of multiplicative congruential random number generators with modulus 2^ 31-1", SIAM J. Sci. Stat. Comput., Vol 7, No 1, pp. 24-45, jan. 1986.

21
Fushimi M. and S. Tezuka : "The k-distribution of generalized feedback shift register pseudorandom numbers", Communications of the ACM, Vol 26, No 7, pp. 516-523, jul. 1983.

22
Fushimi M. : "Designing a uniform random number generator whose subsequences are k-distributed", SIAM J. Comput., Vol 17, No 1, pp. 89-99, feb. 1988.

23
Fushimi M. : "Random number generation on parallel processors", Proc. of the 1989 WSC, pp. 459-461, 1989.

24
Gallager R.G. : "Variations on a Theme by Huffman", IEEE Transactions on Information Theory, Vol 24, No 6, pp. 668-674, nov. 1978.

25
Goldreich O., H. Krawczyck and M. Luby : "On the existence of pseudo random generators", IEEE Symposium on the Foundations of Computer Science, 29th SFCS, pp. 12-24, 1988.

26
Hardy G.H. and E.M. Wright : "An introduction to the theory of numbers, fifth edition". Oxford, 426 p., 1979.

27
Hemmati F. : "Large Class of Non Linear Shift Register Sequences", IEEE Transactions on Information Theory, Vol 28, No 2, pp. 355-359, mar. 1982.

28
Knuth D.E. : "The art of computer programming", Vol 2 : "Semi-numerical Algorithms", 2nd Edition, Addison-Wesley, Reading, Mass., 1981.

29
Knuth D.E. : "Deciphering Linear Congruential Encryption", IEEE Transactions on Information Theory, Vol 31, No 1, pp. 49-52, jan. 1985.

30
L'Ecuyer P. : "An Efficient and Portable Combined Random Number Generator", Comm. of the ACM, Vol 31, No 6, pp. 742/749, jun. 1988.

31
L'Ecuyer P. and R. Proulx : "About polynomial-time 'unpredictable' generators", Proc. of the 1989 WSC, pp. 467-476, 1989.

32
L'Ecuyer P. : "Random number generation for simulations", Comm. of the ACM, Vol 33, No 10, pp. 86-97, oct. 1990.

33
L'Ecuyer P. : "Testing random number generators", Proc. of the 1992 WSC, pp. 305-313, 1992

34
L'Ecuyer P. : "Recent advances in uniform random number generation", Proc. of the 1994 WSC, pp. 122-132, 1994.

35
L'Ecuyer : "Uniform random number generators : a review", Proc of the 1997 WSC, 8 p., 1997.

36
L'Ecuyer P., A. Compagner and J.F. Cordeau : "Entropy tests for random number generators", submitted to ACM TOMACS, 1997.

37
L'Ecuyer P. : "Random number generation", chap. 4 of "Handbook of simulation", J. Banks ed, 864 p., J. Wiley & Sons, sep. 1998.

38
Leva J.L. : "A fast normal random number generator", ACM Trans. on Math. Software, Vol 18, No 4, pp. 449-453, 1992.

39
Lewis T. and W. Payne : "Generalized feedback shift register pseudo random number algorithms", Journal of the ACM, Vol 20, No 3, pp. 456-468, jul. 1973.

40
MacLaren M. D. and G. Marsaglia : "Uniform random number generators", J. of the ACM, Vol 12, No 1, pp. 83-89, jan. 1965.

41
Marsaglia G. and T. Bray : "One-line random number generators and their use in combination", Communications of the ACM, Vol 11, No 11, pp. 757-759, nov. 1968.

42
Marsaglia G. : "The structure of linear congruential sequences", pp. 249-285 in Applications of Number Theory to Numerical Analysis. Z. K. Zaremba, Ed., Academic Press, New York, 1972.

43
Marsaglia G. : "A current view of random number generators", Proc. of the 16th Symposium on the Interface, 11 p., Atlanta, 1984.

44
Marsaglia G. : "Monkey tests for random numbers generators", Computers and Mathematics with Applications, Vol 9, pp. 1-10, 1993.

45
Marsaglia G. : "Multiply-with-carry generators", mwc1.ps in "diehard.zip", 1998.

46
Mertsch M.K. : "On performance analysis and selection criteria of random number generators for simulations", Telatrafic Science for New Cost-Effective Systems, Networks and Services, ITC-12, pp. 1291-1297.

47
Niederreiter H. : "Statistical Analysis of Generalized Feedback Shift Register Pseudorandom Number Generators", SIAM Journal on Scientific and Statistical Computing, Vol 08, No 6, pp. 1035-1051, nov. 1987.

48
Niederreiter H. : "New methods for pseudo-random number and pseudo-random vector generation", Proc. of the 1992 WSC, pp. 264-269, 1992.

49
Park S. and K. Miller : "Random Number Generators: Good Ones Are Hard to Find", Communications of the ACM, Vol 31, No A, pp. 1192-201, oct. 1988.

50
Reif J.H. and J.D. Tygar : "Efficient Parallel Pseudo Random Number Generation", SIAM Journal on Computing, Vol 17, No 4, pp. 404-411, apr. 1988.

51
Ritter T. : "The Efficient Generation of Cryptographic Confusion Sequences", Cryptologia, Vol 15, No 2, pp. 81-139, apr. 1991.

52
Ritter T. : "Substitution Ciphers With Pseudo Random Shuffling: Dynamic Substitution Combiner", Cryptologia, Vol 14, No 4, pp. 289-303, oct. 1990.

53
Ritter T. : "Transposition Cipher With Pseudo Random Shuffling: Dynamic Transposition Combiner", Cryptologia, Vol 15, No 1, pp. 001-016, jan. 1991.

54
Rueppel R.A. and O.J. Staffelbach : "Products of Linear Sequences With Maximal Complexity", IEEE Transactions on Information Theory, Vol 33, No 1, pp. 124-131, jan. 1987.

55
Tezuka S. : "Discrepancy of GFSR Pseudo Random Numbers", Journal of the ACM, Vol 34, No 4, pp.   939-949, oct. 1987.

56
Tezuka S. : "Walsh Spectral Test For GFSR Pseudorandom Numbers", Communications of the ACM, Vol 30, No 8, pp. 731-735, aug. 1987.

57
Tezuka S. : "Neave effects also occurs with tausworthe sequences", Proc of the 1991 WSC, pp. 1030-1034.

58
Tezuka S. and P. Lecuyer : "Analysis of add-with-carry and substract-with-borrow generators", Proc of the 1992 WSC, pp. 443-447, 1992.

59
Tootill J., W. Robinson and A. Adams : "The runs up-and-down Performance of Tausworthe pseudo-random Number Generators", Journal of the ACM, Vol 18, No 3, pp. 381-399, jul. 1971.

60
Tootill J., W. Robinson and D. Eagle : "Asymptotically Random Tausworthe Sequence", Journal of the ACM, Vol 20, No 3, pp. 469-481, jul. 1973.

61
Westlake W. : "Uniform Random Number Generator Based on the Combination of Two Congruential Generators", Journal of the ACM, Vol 14, No 2, pp.  337-340, avr. 1967.

62
Whittlesey J.R.B. : "On the multidimensional uniformity of pseudorandom number generators", Communications of the ACM, Vol 12, No 5, p. 247, may. 1969.

63
-----------------------------

64
Arvillias A.C. and A.E. Maritsas : "Partitioning the period of m-sequences and applications to pseudorandom number generation", J. ACM 25, 675-686, (1978).

65
Bright H.J. and R.L. Enison : "Quasi-random number sequences from a long period TLP generator with remarks on applications to cryptography". Computing Surveys 11, pp. 357-370, 1979.

66
Brown M. and H. Solomon : "On combining pseudorandom number generators", Technical Report No. 233, Dept. of Statistics, Stanford University, 1976. Also Annals of Statistics, Vol 1, pp. 691-695. *** X W2a18a

67
Compagner A. and A. Hoogland : "Maximum Length Sequences, Cellular Automata and Random Numbers", Journal on Computational Physic, Vol 71, No ..., pp. 391-428, .... 1987.

68
Collings B.J. : "Compound Random Number Generators", Journal of the American Statistical Association, JASA-82, No ..., pp. 525-527, 398. 1987.

69
Goldreich O., S. Goldwasser and S. Micali : "How to Construct Random Functions", IEEE Symposium on the Foundations of Computer Science, 25th SFCS, pp. 464-479, 1984.

70
Hastad J. and A. Shamir : "Cryptographic Security of Truncated Linearly Related Variables", ACM Symposium on Theory of Computing, 17th STC, pp. 356-362, 1985.

71
Kendall D.G. and B. Babington-Smith : "Randomness and random sampling numbers", J. Royal Statist. Soc. 101 pp. 146- 166, 1938. See also J. Royal Statist. Soc. Supplement 6, pp 51-36, 1939.

72
Letham L., D. Hoff and A. Folmsbee : "Eprom(128k) Using Encryption Of Pseudorandom Numbers to Enable Read Access", IEEE Journal on Solid-State Circuit, Vol 21, No ., pp.881-888, .... 1986.

73
Lewis P.A., A.S. Goodman and J.M. Miller : "A pseudo-random number generator for the System/360, IBM Syst. J. ,Vol 8, No 2, pp. 136-146, 1969.

74
Marsaglia G. : "Random numbers fall mainly in the planes", Proceedings National Academy Science 61, pp. 25-28, 1968. *** X W2a35

75
Marsaglia G. and L. H. Tsay : "Matrices and the structure of random number sequences", Linear Algebra and Its Applications 67, pp. 147-156, 1985.

76
Marshall A.W., and I. Olkin : "Inequalities: Theory of Majorization and its Applications", Academic Press, New York, 1979.

77
Meyer C. and S. Matyas : "Cryptography: A New Dimension in Computer Data Security", Wiley & Sons, 1982.

78
Mitchell D. : "Non Linear Key Generators", Cryptologia, Vol 14, No ., pp. 350-354, .... 1990.

79
Reeds J. : " Cracking Random Number Generator", Cryptologia, Vol 01, No 1, pp. 20/26, jan. 1977.

80
Retter C. : "A Key Search Attack on Maclaren Marsaglia Systems", Cryptologia, Vol 09, No ., pp.   l14-130,.... 1985.

81
Retter C. : "Cryptanalysis of a Maclaren Marsaglia System", Cryptologia, Vol 08, No ., pp. 97 &374, .... 1984.

82
Rubin F. : "Decrypting Stream Cipher Bawd On J-k Flip Flops (IC-28 P483 -487)", Cryptologia, Vol   05, No 1, pp. 51-57, jan. 1979.

83
Rubin F. : "Computer Methods for Decrypting Random Stream Ciphers", Cryptologia, Vol 02, No   3, pp. ... , apr. 1978.

84
Vahle M. and L. Tolendino : " Breaking Pseudo Random Number Based Cryptographic Algorithm", Cryptologia, Vol  06, No ..., pp. 319-328, .... 1982.

85
------ new --------


previous up next contents index
Previous: 1.9 En conclusion Up: Simulations Next: 2. Générateurs non uniformes   Contents   Index


douillet@ensait.fr
2005-01-04