The paper presents new quantum-resistant public-key cryptosystems based on the hardness of finding isogenies between supersingular elliptic curves. The main technical idea is to transmit the images of torsion bases under the isogeny to allow parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. The authors provide a precise formulation of the necessary computational assumptions and prove the security of their protocols under these assumptions. They also present implementation results showing that their protocols are significantly faster than previous isogeny-based cryptosystems over ordinary curves. The paper includes a new zero-knowledge identification scheme and detailed security proofs for the protocols, as well as an asymptotically faster algorithm for key generation and experimental data. The proposed scheme is based on new computational assumptions and offers promising performance and security improvements over existing quantum-resistant cryptosystems.The paper presents new quantum-resistant public-key cryptosystems based on the hardness of finding isogenies between supersingular elliptic curves. The main technical idea is to transmit the images of torsion bases under the isogeny to allow parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. The authors provide a precise formulation of the necessary computational assumptions and prove the security of their protocols under these assumptions. They also present implementation results showing that their protocols are significantly faster than previous isogeny-based cryptosystems over ordinary curves. The paper includes a new zero-knowledge identification scheme and detailed security proofs for the protocols, as well as an asymptotically faster algorithm for key generation and experimental data. The proposed scheme is based on new computational assumptions and offers promising performance and security improvements over existing quantum-resistant cryptosystems.