Inversive Congruential Generator The inversive congruential generator over the prime field $k=Z/pZ$ is given by the iterations of the map $x\mapsto a/x+b$ if $x\neq 0$ or $b$ if $x=0$.
One can choose $a,b$ in $k$ such that the orbit length of the iteration is exactly $p$. My question is very simple:

Is the Inversive Congruential Generator actually used in Cryptography? Is there any known attack against it?
The inversive congruential generator is not commonly used in cryptography. Its basic description, in fact, makes it entirely unsuitable for it—once you know a single value of $x$, you can predict the remainder of the sequence, which is something a secure pseudorandom generator should not allow.

To avoid the above trivial attack, you could truncate the output to, say, half of the bits of $x$. But the truncated inversive generator is also predictable by more elaborate means, as long as you truncate fewer than half the bits.

To top it off, inversion modulo $p$ is a very slow operation, which makes this generator very inefficient. So even for non-cryptographic purposes this is not a good generator to use.