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Isogeny Secrets can be Traded

We consider a situation in which two mutually distrusting parties, each possessing a secret piece of information, wish to exchange these secrets while communicating over a secure channel, in effect “trading” them. Each is afraid of counterparty risk: Alice fears that as soon as she sends her secret to Bob he will cease communication without sending his secret in return, and likewise for the reverse case. In the situation where Alice and Bob’s secrets are protected by isogenies, we propose a system in which Alice and Bob may fairly exchange their secrets without counterparty risk, and without a trusted third party. We then discuss potential applications.