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The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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On the Generation of Cryptographically Strong Pseudo-Random Sequences
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STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Inferring sequences produced by pseudo-random number generators
Inferring sequences produced by pseudo-random number generators
Inferring sequences produced by pseudo-random number generators
Inferring sequences produced by pseudo-random number generators
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CRYPTO '89 Proceedings on Advances in cryptology
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CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
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PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
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A generator of pseudo-random numbers sequences with maximum period
ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
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Reconstructing noisy polynomial evaluation in residue rings
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Quantum period reconstruction of approximate sequences
Information Processing Letters
Designs, Codes and Cryptography
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Computer Communications
On stern's attack against secret truncated linear congruential generators
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
A generator of pseudo-random numbers sequences with a very long period
Mathematical and Computer Modelling: An International Journal
Inferring sequences produced by nonlinear pseudorandom number generators using coppersmith's methods
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Predicting masked linear pseudorandom number generators over finite fields
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Proceedings of the 23rd ACM international conference on Great lakes symposium on VLSI
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In this paper, efficient algorithms are given for inferring sequences produced by certain pseudo-random number generators. The generators considered are all of the form Xn = &Sgr;kj-l &agr;j&phgr;j(Xo, Xl, . . ., Xn-l) (mod m). In each case, we assume that the functions &phgr;j are known and polynomial time computable, but that the coefficients aj and the modulus m are unknown. Using this general method, specific examples of generators having this form, the linear congruential method, linear congruences with n terms in the recurrence, and quadratic congruences are shown to be cryptographically insecure.