Spontaneous anonymous group (SAG) cryptography is a fundamental alternative to achieve thresholding without group secret or setup. It has gained wide interests in applications to ad hoc groups. We present a general construction of blind SAG 1-out-of-n and t-out-of-n signature schemes from essentially any major blind signature. In the case when our scheme is built from blind Schnorr (resp. Okamoto-Schnorr) signature, the parallel one-more unforgeability is reduced to Schnorr's ROS Problem in the random oracle model plus the generic group model. In the process of our derivations, we obtain a generalization of Schnorr's result from single public key to multiple public keys.