Predicting the Inversive Generator
نویسندگان
چکیده
Let p be a prime and let a and b be integers modulo p. The inversive congruential generator (ICG) is a sequence (un) of pseudorandom numbers defined by the relation un+1 ≡ au−1 n + b mod p. We show that if b and sufficiently many of the most significant bits of three consecutive values un of the ICG are given, one can recover in polynomial time the initial value u0 (even in the case where the coefficient a is unknown) provided that the initial value u0 does not lie in a certain small subset of exceptional values.
منابع مشابه
Inversive Congruential Pseudorandom Numbers Avoid the Planes
Nonlinear congruential pseudorandom number generators based on inversions have recently been introduced and analyzed. These generators do not show the lattice structure of the widely used linear congruential method. In the present paper it is proved that the points formed by d consecutive pseudorandom numbers of an inversive congruential generator with prime modulus possess an even stronger pro...
متن کاملOn a nonlinear congruential pseudorandom number generator
A nonlinear congruential pseudorandom number generator with modulus M = 2w 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.
متن کاملPredicting nonlinear pseudorandom number generators
Let p be a prime and let a and b be elements of the finite field Fp of p elements. The inversive congruential generator (ICG) is a sequence (un) of pseudorandom numbers defined by the relation un+1 ≡ au−1 n +b mod p. We show that if sufficiently many of the most significant bits of several consecutive values un of the ICG are given, one can recover the initial value u0 (even in the case where t...
متن کاملCompound Inversive Congruential Generator Design Algorithm
In this paper we present an algorithm for the compound method of designing generators as pseudorandom stream sources. Compound method relies on a technique of combining two or more inversive congruential generators. Experiments on congruential methods showed that even if all tested generators have maximum period not all produced binary sequences have the linear complexity of the same value. We ...
متن کاملPseudorandom Number Generation by Inversive Methods
The classical linear congruential method for generating uniform pseudorandom numbers has some deficiencies that can render them useless for some simulation problems. This fact motivated the design and analysis of nonlinear congruential methods for the generation of pseudorandom numbers. Inversive methods are an interesting and very promising approach to produce uniform pseudorandom numbers. We ...
متن کامل