Séminaire de Cryptographie

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Pauline Bert

Lattice-based signatures: from construction to implementation

Lattice-based cryptography is one of the major line of research to build post-quantum public key primitives. In this thesis, we discuss about digital signatures constructions and their implementation. We first describe a Fiat-Shamir transformation from an identification scheme using rejection sampling to a digital signature secure in the random oracle model. Then we describe an identity-based encryption scheme and we prove its security in the standard model. An identity-based encryption scheme is like a classical public key where the public key is the identity of a user such as its email address or its social security number. A user contacts a third trusted party to get a secret key associated to its identity. In our construction, a secret key consists essentially in a signature of the identity of the user. We also describe this underlying digital signature scheme associated to our identity based encryption scheme. Finally, we present implementation results of these two schemes and how we choose concrete parameters.