Consider a group of $n$ public keys $pk_1,...,pk_n$ with corresponding secret keys $sk_1,...,sk_n$.
I'm looking for a cryptographic primitive with the following properties:
Ring signature property.
It allows the owner of a secret key $sk_i$ to digitally sign a message in anonymous way i.e., any one validating the signature can know it validly signed by one of $pk_1,...,pk_n$ and no additional information is known about the signer.
Any group of $t$ different secret key holders out of the group of $n$ holders can collaborate and reveal who is the true signer.
No trusted setup.
The third property is not strict and can be relaxed.
Does anyone knows anything that may fit this properties?