Paper 2018/459

Revisiting SIOT protocol with new security assumptions

Abstract

Oblivious Transfer is one of the most important building blocks in cryptography and useful for building secure protocols. With the advent of quantum computing there was a boost in research and development of cryptographic protocols resistant to quantum computer processing. Thus, in 2018, the SIOT (Supersingular Isogeny Oblivious Transfer) protocol was presented as the first post-quantum cryptographic OT scheme based on supersingular elliptic curve isogenies. Initially, an OT scheme was created combined with the cryptographic primitives of the SIDH (Supersingular Isogeny Diffie-Hellman) protocol. Furthermore, the SIOT protocol was built in its simplest configuration against semi-honest adversaries. However, it was subjected to scrutiny that resulted in the need to develop new security proofs. Almost in parallel, new and efficient cryptanalytic attacks emerged on the SIDH protocol, which consequently compromised the SIOT security structure. Thus, the new definitions of security proofs encompassed the compatibility of certain parameters of the OT functionality of the SIOT protocol itself with security assumptions of computational isogeny problems. After that, the security countermeasures from M-SIDH (Masked-Supersingular Isogeny Diffie-Hellman) protocol were analysed and implemented into SIOT protocol. Therefore, we propose an OT protocol based on isogenies of elliptic curves and with resistance to quantum attacks.

Note: New proofs have been implemented to support the security of the protocol. Although this cryptographic protocol does not have a practical application, the authors hope that the specific subject of OT protocols with elliptic curve isogenies will continue to arouse scientific-academic interest for future improvements and discoveries.