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Inversive Congruential Pseudorandom Numbers: Distribution Of Triples
, 1997
"... This paper deals with the inversive congruential method with power of two modulus m for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that, on th ..."
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Cited by 40 (0 self)
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This paper deals with the inversive congruential method with power of two modulus m for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that, on the average over the parameters in the inversive congruential method, the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude between m \Gamma1=2 and m \Gamma1=2 (log m)³. The method of proof relies on a detailed discussion of the properties of certain exponential sums.
How to Stretch Random Functions: The Security of Protected Counter Sums
 Journal of Cryptology
, 1999
"... . Let f be an unpredictable random function taking (b + c)bit inputs to bbit outputs. This paper presents an unpredictable random function f 0 taking variablelength inputs to bbit outputs. This construction has several advantages over chaining, which was proven unpredictable by Bellare, Ki ..."
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Cited by 21 (8 self)
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. Let f be an unpredictable random function taking (b + c)bit inputs to bbit outputs. This paper presents an unpredictable random function f 0 taking variablelength inputs to bbit outputs. This construction has several advantages over chaining, which was proven unpredictable by Bellare, Kilian, and Rogaway, and cascading, which was proven unpredictable by Bellare, Canetti, and Krawczyk. The highlight here is a very simple proof of security. 1.
On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period
 Math. Comp
, 2000
"... Abstract. The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in p ..."
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Cited by 10 (4 self)
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Abstract. The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period. The proof is based on a new bound for certain incomplete exponential sums. 1.
On a nonlinear congruential pseudorandom number generator
 Math. Comp
, 1996
"... Abstract. A nonlinear congruential pseudorandom number generator with modulus M =2 w is proposed, which may be viewed to comprise both linear as well as inversive congruential generators. The condition for it to generate sequences of maximal period length is obtained. It is akin to the inversive one ..."
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Cited by 2 (1 self)
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Abstract. A nonlinear congruential pseudorandom number generator with modulus M =2 w is proposed, which may be viewed to comprise both linear as well as inversive congruential generators. The condition for it to generate sequences of maximal period length is obtained. It is akin to the inversive one and bears a remarkable resemblance to the latter. 1.
Analysis of PseudoRandom Properties of Nonlinear Congruential Generators with Power of Two Modulus by Numerical Computing of the badic
"... Abstract—We consider two nonlinear methods for generating uniform pseudorandom numbers in [0, 1), namely quadratic congruential generator and inversive congruential generator. The combinations of the Van der Corput sequence with the considered nonlinear generators are proposed. We simplify the mixe ..."
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Abstract—We consider two nonlinear methods for generating uniform pseudorandom numbers in [0, 1), namely quadratic congruential generator and inversive congruential generator. The combinations of the Van der Corput sequence with the considered nonlinear generators are proposed. We simplify the mixed sequences by a restriction of the badic representation of the points. We study numerically the badic diaphony of the nets obtained through quadratic congruential generator, inversive congruential generator, their combinations with the Van der Corput sequence, and the simplification of the mixed sequences. The value of the badic diaphony decreases with the increase of the number of the points of the simplified sequences which proves that the points of the simplified sequences are pseudorandom numbers. The analysis of the results shows that the combinations of the Van der Corput sequence with these nonlinear generators have good pseudorandom properties as well as the generators. I.