Séminaire de Cryptographie

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Luca De Feo

Open problems in isogeny-based cryptography

Isogeny-based cryptography (IBC) is a very young field, only 10 years old. Protocols in this family include key-exchange, encryption, "provably secure" hash functions and trapdoor systems. Hardness assumptions in IBC come from the difficulty of finding paths in isogeny graphs, that is graphs of elliptic curves linked by isogenies of some prescribed degree. Recently some IBC protocols have raised a wave of interest thanks to their resistance to quantum attacks and their compact key size. This talk will review the essential topics in IBC and list some open problems, in a way accessible to the non-specialist.