Lack of usage of secrets in ZK Bitcoin ownership proof
Yes, $\Sigma$-protocol is described at section 4.1 of the paper referenced. This is a 3-move protocol, with the last message "response" computed from second message "challenge" and a secret. In particular, 4 responses are computed at step 1(d) of the protocol presented. Coin private keys $x_i$ held by exchange is the input for computing the last response, selected by binary mask $s_i \in \{0, 1\}: \; \hat x_i = x_i s_i$.