The digital signature schemes that have been proposed so far in the setting of the Supersingular Isogeny Diffie-Hellman scheme (SIDH) were obtained by turning an interactive identification protocol by De Feo, Jao and Plût into non-interactive schemes. The security of the resulting schemes is therefore deduced from that of the base identification protocol. In this talk, we revisit the proofs that have appeared in the literature for the special soundness property of the above-mentioned SIDH-based identification protocol. The existence of some special cycles in supersingular isogeny graphs make such previous proofs fail.