Organizer: Stefanie Kettler, CROSSING
In their recent work , DeFeo and Meyer introduced a method for executing isogeny based public key encryptions on a private key, that had been stored in Shamir’s information theoretical secret sharing scheme . While their approach enables a distributed en- and decryption for a threshold scheme, it is rather restrictive in that the access structure is limited to sets of a minimum size and lacks granularity. Furthermore their approach is only passively secure, i.e., a misbehaving adversary cannot be detected.
In this work we elevate ’s scheme to an actively secure setting, that is misbehaving player’s are detected while the protocol is being executed. Furthermore we expand the range of secret sharing schemes able to support DeFeo’s and Meyer’s approach by defining some characterising properties of suitable schemes. We also prove that for schemes with said properties the same security guarantees hold in regards to ’s approach. Furthermore we show that Shamir’s scheme has our generalised properties, and thereby our approach truly is a generalisation of .
Finally, we give examples of more elaborate secret sharing schemes, respectively access structures, that are enabled by our approach.