There are some protocols, e.g. this, that require parties to compute/use RSA modulus: $N$ without knowing it's factors or $\phi(N)$.

One way of doing it is to use a trusted party.

Question: Is there any other way of generating/using $N$ in the above schemes without using a trusted party? (If yes, can you refer me to some papers)

up vote 1 down vote accepted

It is possible to do this with secure multiparty computation. There are several papers about this problem, but the most recent state of the art is:

Tore Kasper Frederiksen and Yehuda Lindell and Valery Osheter and Benny Pinkas: Fast Distributed RSA Key Generation for Semi-Honest and Malicious Adversaries

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