In this report we study the pi-calculus with polyadic synchronization: an extension of the pi-calculus that generalizes the synchronization mechanism by allowing channels to be sequences of names. In particular, we extend the pi-calculus with polyadic synchronization with cryptographic primitives and then prove the last can be encoded in the regular pi-calculus with polyadic synchronization. Further, we prove that the proposed encoding is sound and complete with respect to barbed congruence which we show coincides with early congruence.