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I'm looking for some PRNGs and – as I have been using Java for a long period of time – I thought that the BitInteger class, together with the Random class, could both generate some large pseudo random numbers.

Are the algorithms behind those generations cryptographically secure, or is it just some sort of a + (b - c) mod d or similar operation?

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Exactly what algorithms are you considering in the phrase of the question ending in a question mark? –  fgrieu Mar 24 '12 at 9:01
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Just use the SecureRandom class. –  CodesInChaos Mar 24 '12 at 9:49
    
I was considering the algorithms behind the Random and BigInteger class. –  vlad Mar 30 '12 at 11:18
    
@vlad you were considering wrong :) –  owlstead Apr 5 '12 at 1:27
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BigInteger does not contain PRNG code at all. It uses RNGs only. Btw, the statement to use SecureRandom is even in the JavaDoc of the Random class. Last sentence of the first paragraph –  tylo Jun 12 at 10:53

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up vote 6 down vote accepted

Presuming this documentation is correct, the answer is no, these numbers are not cryptographically secure. The Random class uses a linear congruential formula with a 48 bit seed. For most purposes it is not enough even if you only require 48 bit security. Given a fairly low number of outputs from a LCG, it is possible to derive the seed, even if only a few bits of each seed iteration are used. That question has been answered here.

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