Papers on random number generation

  1. The paper proposing MT

    M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator", ACM Trans. on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 (1998) DOI:10.1145/272991.272995

  2. MT's previous form TGFSR I

    M. Matsumoto and Y. Kurita, "Twisted GFSR generators", ACM Trans. on Modeling and Computer Simulation, 2(1992),179--194 DOI:10.1145/146382.146383
    tgfsr3.pdf (pdf)

  3. MT's previous form TGFSR II

    M. Matsumoto and Y. Kurita, "Twisted GFSR generators II", ACM Trans. on Modeling and Computer Simulation, 4(1994),254--266 DOI:10.1145/189443.189445
    ttgfsr7.pdf (pdf file)

  4. Dynamic Creator: Generate independent Mersenne Twisters dynamically, for parallel computation.

    Makoto Matsumoto and Takuji Nishimura, "Dynamic Creation of Pseudorandom Number Generators", Monte Carlo and Quasi-Monte Carlo Methods 1998, Springer, 2000, pp 56--69. dgene.ps or dgene.pdf.

  5. SIMD-oriented Fast Mersenne Twister,

    Mutsuo Saito and Makoto Matsumoto, "SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator", Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, 2008, pp. 607 -- 622.     DOI:10.1007/978-3-540-74496-2_36
    sfmt.pdf
    Some mistakes of figures are found on dimension of equi-distribution value. Please see Errata. (Sep. 1st. 2015)
    See Mutsuo Saito's Master's Thesis for more detailed informatiom.

  6. WELL pseudo random number generator

    F. Panneton, P. L'Ecuyer and M. Matsumoto "Improved Long-Period Generators Based on Linear Reccurences Modulo 2", ACM Transactions on Mathematical Software, 32 (1, March) 2006, 1--16.     DOI:10.1145/1132973.1132974
    see also Pierre L'Ecuyer's publications No. 30.

  7. Generating multiple disjoint streams of pseudorandom number sequencesJump

    Hiroshi Haramoto, Makoto Matsumoto, and Pierre LfEcuyer, "A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space", Sequences and Their Applications - SETA 2008, 290--298,     DOI:10.1007/978-3-540-85912-3_26
    pre-print.pdf

  8. Generating multiple disjoint streams of pseudorandom number sequences

    Hiroshi Haramoto, Makoto Matsumoto, Takuji Nishimura, François Panneton, Pierre LfEcuyer, "Efficient Jump Ahead for F2-Linear Random Number Generators", INFORMS JOURNAL ON COMPUTING, Vol. 20, No. 3, Summer 2008, pp. 385-390     DOI: 10.1287/ijoc.1070.0251
    author copy

  9. A PRNG Specialized in Double Precision Floating Point Number Using an Affine Transition

    Mutsuo Saito and Makoto Matsumoto, Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer, 2009, pp. 589 -- 602.     DOI:10.1007/978-3-642-04107-5_38
    dSFMT.pdf
    Some mistakes of figures are found on dimension of equi-distribution value. Please see Errata. (Sep. 28th. 2015)

Theoretical Tests on Randomness

  1. M. Matsumoto and Y. Kurita, "Strong deviations from randomness in m-sequences based on trinomials," ACM Trans. on Modeling and Computer Simulation, 6 (1996), pp 99-106. devi.pdf (pdf file)
  2. M. Matsumoto and T. Nishimura ``A Nonempirical Test on the Weight of Pseudorandom Number Generators'' 381--395 in: Monte Carlo and Quasi-Monte Carlo methods 2000, Ed. K.T. Fang, F.J.Hickernel, and H. Niederreiter, Springer-Verlag 2002. hong-fin4.pdf.
  3. M. Matsumoto and T. Nishimura ``Sum-discrepancy test on pseudorandom number generators'' Mathematics and Computers in Simulation, Vol. 62 (2003), pp 431-442. DOI:10.1016/S0378-4754(02)00227-6
    mnsalz8.pdf
  4. Makoto Matsumoto, Mutsuo Saito, Hiroshi Haramoto, Takuji Nishimura "Pseudorandom Number Generation: Impossibility and Compromise", Journal of Universal Computer Science, Vol. 12, No. 6, pp. 672-690, 2006.
  5. M. Matsumoto and T. Nishimura, "Weight discrepancy tests on M-sequences", Bulltin of Yamagata University (Natural Science), Vol. 16, No.3, 2007, 105--112.
  6. Haramoto, H., Matsumoto, M., Nishimura, T. "Computing conditional probabilities for F2-linear pseudorandom bit generator by splitting Mac-Williams identity", International Journal of Pure and Applied Mathematics, Vol.38 No.1, 2007.
  7. Makoto Matsumoto, Isaku Wada, Ai Kuramoto, Hyo Ashihara, "Common Defects in Initialization of Pseudorandom Number Generators", ACM Trans. on Modeling and Computer Simulation 17(4): 2007. Article No. 15, DOI:10.1145/1276927.1276928

Cryptography

  1. CRYPTOGRAPHIC MERSENNE TWISTER AND FUBUKI STREAM/BLOCK CIPHER

  2. About theoretical side of CryptMT ver. 3

    Matsumoto, M., Saito, M., Nishimura, T. and Hagita, M. "A Fast Stream Cipher with Huge State Space and Quasigroup Filter for Software", Selected Areas in Cryptography 2007, Lecture Notes in Computer Science (LNCS), vol. 4876, pp. 246 -- 263, 2007. DOI:10.1007/978-3-540-77360-3_16
    sac2007.pdf

  3. CryptMT ver. 3

    Matsumoto, M., Saito, M., Nishimura, T. and Hagita, M. "CryptMT3 Stream Cipher", New Stream Cipher Designs, Lecture Notes in Computer Science (LNCS), vol. 4986, pp. 7 -- 19, 2008. DOI:10.1007/978-3-540-68351-3_2
    PDF

Other

"Simple cellular automata as pseudorandom m-sequence generators for built-in self-test"
M. Matsumoto, ACM Transactions on Modeling and Computer Simulation 8. (Jan. 1998) 31-42. DOI:10.1145/272991.273007
rng8.pdf (pdf file)

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