| Your friend is not going to get PhD thesis topics by asking his friend to post on HN. Regardless, here's what I think are interesting areas in recent crypto: - Performance improvements in fully homomorphic encryption, starting with Gentry's work in 2009. - Practical applications of secure multiparty computation, e.g. Dyadic Security and Google's SMC work. - Non-NIST standards with actual adoption like Curve25519 and Chacha20-Poly1305 - Functional Encryption: http://eprint.iacr.org/2010/543 - Post-quantum crypto like New Hope (https://eprint.iacr.org/2015/1092) and Supersingular Isogenies (http://eprint.iacr.org/2011/506) - Candidate functions for Multilinear Maps, e.g. https://eprint.iacr.org/2012/610 - Hardware-based secure enclaves like SGX |