Authenticated logarithmic-order supersingular isogeny group key exchange

We present the first constant-round, tree-based, group key exchange protocol based on SIDH with logarithmic-order communication and memory complexity, where only previous isogeny-based exchange, SIBD, has linear-order complexity. call our supersingular isogeny tree-based (SIT). show that satisfies post-quantum security through a reduction to decisional Diffie–Hellman (SSDDH) problem in model of Manulis, Suzuki, Ustaoglu. also construct peer-to-peer (sequential) version SIT. Finally, we compiler turns SIT into an authenticated while maintaining same complexity as SIT, resulting (A-SIT).