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The ISAAC site claims it is secure, but I wasn't aware of any trusted 3rd party sources that verified its security.

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It's actually fairly good. Unlike the previous post it was actually published in Fast software encryption about 15 years ago. It's still being looked at actively and has held up fairly well. The best attack against it was done by Auasson in 08. The major issue is on the way which it is initially seeded.

ISAAC has been partially superseeded by ISAAC+ to deal with some of the issues Aumasson pointed out. It still works fairly well.

For random number generators you can't really "verify" you can say it looks pretty good.

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I had a short look at the page - it contains only some implementations, no specification.

The page ISAAC and RC4 from the same author contains some theoretical elaboration about ISAAC and its relatives IA and IBAA, but I'm not sure if this can be called specification.

Non-existence of a formal specification is a major drawback for anything which claims to be a serious cryptographic algorithm, and might be the deciding reason that nobody really looked at the security of this primitive.

So my recommendation would be to use other, better documented algorithms instead, if security is of importance (and not only speed).

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