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AbstractWe present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. We give a precise formulation of the necessary computational assumptions along with adoi:10.1515/jmc-2012-0015 fatcat:rvwrwr7azndrbmbjy5ln3ylxfq