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Predicting masked linear pseudorandom number generators over finite fields

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Abstract

We study the security of the linear generator over a finite field. It is shown that the seed of a linear generator can be deduced from partial information of a short sequence of consecutive outputs of such generators.

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References

  1. Blackburn S.R., Gómez-Perez D., Gutierrez J., Shparlinski I.E.: Predicting the inversive generator. Lecture Notes in Computer Science, vol. 2898, pp. 264–275. Springer, Berlin (2003).

  2. Blackburn S.R., Gómez-Perez D., Gutierrez J., Shparlinski I.E.: Predicting nonlinear pseudorandom number generators. Math. Comput. 74, 1471–1494 (2005)

    MATH  Google Scholar 

  3. Blum L., Blum M., Shub M.: A simple unpredictable pseudo-random number generator. SIAM J. Comput. 15, 364–383 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boyar J.: Inferring sequences produced by pseudo-random number generators. J. ACM 36, 129–141 (1989a)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boyar J.: Inferring sequences produces by a linear congruential generator missing low-order bits. J. Cryptol. 1, 177–184 (1989b)

    Article  MathSciNet  MATH  Google Scholar 

  6. Contini S., Shparlinski I.E.: On Stern’s attack against secret truncated linear congruential generators. Lecture Notes in Computer Science, vol. 3574, pp. 52–60. Springer, Berlin (2005).

  7. Frieze A.M., Håstad J., Kannan R., Lagarias J.C., Shamir A.: Reconstructing truncated integer variables satisfying linear congruences. SIAM J. Comput. 17, 262–280 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gómez-Perez D., Gutierrez J., Ibeas Á.: Attacking the Pollard generator. IEEE Trans. Inf. Theory 52, 5518–5523 (2006)

    Article  Google Scholar 

  9. Griffin F., Niederreiter H., Shparlinski I.E.: On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. Lecture Notes in Computer Science, vol. 1719, pp. 87–93. Springer, Berlin (1999).

  10. Gutierrez J., Gómez-Perez D.: Iterations of multivariate polynomials and discrepancy of pseudorandom numbers. Lecture Notes in Computer Science, vol. 2227, pp. 192–199. Springer, Berlin (2001).

  11. Gutierrez J., Ibeas Á.: Inferring sequences produced by a linear congruential generator on elliptic curves missing high-order bits. Des. Codes Cryptogr. 41, 199–212 (2007)

    Article  MathSciNet  Google Scholar 

  12. Herrmann M., May A.: Attacking power generators using unravelled linearization: When do we output too much? Lecture Notes in Computer Science, vol. 5912, pp. 487–504. Springer, Berlin (2009).

  13. Joux A., Stern J.: Lattice reduction: a toolbox for the cryptanalyst. J. Cryptol. 11, 161–185 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Knuth D.E.: Deciphering a linear congruential encryption. IEEE Trans. Inf. Theory. 31, 49–52 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  15. Krawczyk H.: How to predict congruential generators. J. Algorithms 13, 527–545 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lidl R., Niederreiter H.: Finite Fields. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  17. Ostafe A.: Multivariate permutation polynomial systems and pseudorandom number generators. Finite Fields Appl. 16, 144–154 (2010a)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ostafe A.: Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers. Lecture Notes in Computer Science, vol. 6087, pp. 62–72. Springer, Berlin (2010b).

  19. Ostafe A., Shparlinski I.E.: On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. Math. Comput. 79, 501–511 (2010a)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ostafe A., Shparlinski I.E.: Pseudorandom numbers and hash functions from iterations of multivariate polynomials. Cryptogr. Commun. 2, 49–67 (2010b)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ostafe A., Pelican E., Shparlinski I.E.: On pseudorandom numbers from multivariate polynomial systems. Finite Fields Appl. 16, 320–328 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Steinfeld R., Pieprzyk J., Wang H.: On the provable security of an efficient RSA-based pseudorandom generator. Lecture Notes in Computer Science, vol. 4284, pp. 194–209. Springer, Berlin (2006).

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Correspondence to Jaime Gutierrez.

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Communicated by D. Panario.

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Gutierrez, J., Ibeas, Á., Gómez-Pérez, D. et al. Predicting masked linear pseudorandom number generators over finite fields. Des. Codes Cryptogr. 67, 395–402 (2013). https://doi.org/10.1007/s10623-012-9615-4

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  • DOI: https://doi.org/10.1007/s10623-012-9615-4

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