Blum Blum Shub Generator. As shown in [2] and [4], LCGs are vulnerable to attacks if they are used to generate keys in a cryptosystem or in similar situations . Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in by Lenore Blum, Manuel Blum and Michael Shub. Blum Blum Shub takes the. Abstract. The asymptotic security of the Blum-Blum-Shub (BBS) pseudo- random generator has been studied by Alexi et al. and Vazirani and Vazi- rani, who.

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This makes the squaring function a bijection on quadratic residues.


Do you have any insight regarding whether the underlying computational hardness assumption will be invalidated by quantum computing? Notify me of new posts via email. Views Read Edit View history. Please help to improve this article by introducing more precise citations.

So if computing quadratic residues is even mildly hard, then predicting the next bit in this random number generator is very hard.

Please help improve it or discuss these issues on the talk page. They were all created by procedural generation. From Wikipedia, the free encyclopedia.

You are commenting using your Facebook account. How does Blum Blum Shub compare with http: I feel that this is the same principle that the Turing test applies to intelligence and is a very old idea in CS.


The following table shows the output in bits for the different bit selection blim used to determine the output. Email required Address never made public. Procedural generation is a widely used term in the production of media; it refers to content generated algorithmically rather than manually.

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You are commenting using your WordPress. The seed x 0 should be an integer that is co-prime to M i. This means we can generate random levels for some kind of games such as roguelike games, making people play randomly generated levels, making a game almost endless. Learn how and when to remove these template messages. Please improve this by adding secondary or tertiary sources.

Two numbers are said to be congruent modulo m when their difference is divisible by m. This page was last edited on 14 Octoberat This article relies too much on references to primary sources. A quick way to find large prime numbers is to pick a random number and apply a probabilistic test for primality. This is often related to computer graphics applications and video game level design source.


Some numbers, likehave very special patterns in their quadratic residues, only 0, 1, and 4 can occur as quadratic residues.

The Blum-Blum-Shub Pseudorandom Generator – Math ∩ Programming

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A pseudorandom number generator is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. There is a proof reducing its security to the computational difficulty of factoring. Also, the greatest common divisor of prime and prime should be a small number, and that is since the greatest common divisor of 46 and 66 is 2.