This paper presents new quantum-resistant public-key cryptosystems based on the difficulty of finding isogenies between supersingular elliptic curves. The authors propose protocols that allow parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. The schemes are based on computational assumptions and are proven secure under these assumptions. Implementation results show that the protocols are significantly faster than previous isogeny-based systems over ordinary curves. The paper also introduces a new zero-knowledge identification scheme and detailed security proofs. The authors also present a new, asymptotically faster algorithm for key generation and provide a thorough study of its optimization. The work is an extension of a previous paper and includes new experimental data. The main technical challenge is overcoming the non-commutativity of the endomorphism ring in the supersingular case. The authors show how to use auxiliary input to protocols to address this issue. The paper also discusses the use of Ramanujan graphs and provides algorithmic details for implementing the protocols efficiently. The proposed schemes are shown to be secure against known quantum attacks and have performance gains due to the faster navigation of supersingular isogeny graphs. The paper concludes with a detailed analysis of the security and efficiency of the proposed protocols.This paper presents new quantum-resistant public-key cryptosystems based on the difficulty of finding isogenies between supersingular elliptic curves. The authors propose protocols that allow parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. The schemes are based on computational assumptions and are proven secure under these assumptions. Implementation results show that the protocols are significantly faster than previous isogeny-based systems over ordinary curves. The paper also introduces a new zero-knowledge identification scheme and detailed security proofs. The authors also present a new, asymptotically faster algorithm for key generation and provide a thorough study of its optimization. The work is an extension of a previous paper and includes new experimental data. The main technical challenge is overcoming the non-commutativity of the endomorphism ring in the supersingular case. The authors show how to use auxiliary input to protocols to address this issue. The paper also discusses the use of Ramanujan graphs and provides algorithmic details for implementing the protocols efficiently. The proposed schemes are shown to be secure against known quantum attacks and have performance gains due to the faster navigation of supersingular isogeny graphs. The paper concludes with a detailed analysis of the security and efficiency of the proposed protocols.