Lattices, Isogenies and Adaptor Signatures in Post-Quantum Cryptography

In this thesis we give an analysis of the hierarchical identity-based broadcast encryption scheme proposed by C. Yang, Zheng, Wang, Lu and Y. Yang. The interest in this scheme is due to the fact that it is one of the few of its kind to be Post-Quantum, and relies on the hardness of the LWE, i.e. on lattice-based problems. For the first time we give a detailed description of the scheme and we present a full introduction to the mathematical and cryptographic background needed to describe it. The main result of the thesis is the construction of an adaptor signature for CSI-FiSh that we called ORCAS. Cryptographic group actions are a promising technique that underlie several Post-Quantum digital signatures, including CSI-FiSh. Our proposal, ORCAS, which stands for One-Round "Cheating" Adaptor Signatures (so named because its pre-signing algorithm resembles how cheating signer might try to forge a Fiat-Shamir-based signature), is directly compatible with CSI-FiSh. While the signatures are produced in a different manner and follow a slightly different distribution, they can still be verified by a blockchain which supports only CSI-FiSh.