The course will study different mathematical assumptions deriving from algebra, number theory,
algebraic geometry, complexity theory and other fields. Example mathematical assumptions include
Decision Diffie Hellman, Pairings, Learning with Errors, Learning Parity with Noise, Quadratic
Residuosity, Multilinear Maps, Obfuscation and such others.
Topics are:
- For each assumption, we will study the structure that gives certain cryptographic functionality
together with the hardness that yields security.
- Example applications include identity-based encryption, functional encryption, homomorphic
signatures, multiparty computation protocols, symmetric key cryptography and hash functions.
- In some surprising applications such as broadcast encryption, attribute-based encryption,
obfuscation, we can even see how different assumptions co-operate with each other to give the
best of both.
