Anna Lysyanskaya's primary research area is cryptography, the study of protecting communication and computation against malicious users. The fundamental problems in this area are secure communication, authentication of data, pseudorandomness, and secure multi-party computation.
Prof. Lysyanskaya wrote her Ph.D. thesis on digital signature schemes and their applications in protocols. Her thesis explores the uses of digital signature schemes in cryptographic protocols, as well as proposes several signature schemes especially suitable for use in protocols.
Cryptography in general, and signature schemes in particular, depends on computational assumptions. A proof that a scheme is unbreakable amounts to showing that solving a certain computational problem is infeasible in any reasonable time. Unconditional proofs of infeasibility of problems relevant to cryptography are not known, and they would imply that P is different from NP. Therefore, in cryptography we have to settle for assumptions that certain tasks are infeasible.
Prof. Lysyanskaya is interested in such issues as efficient and provably secure cryptographic protocols, minimal complexity assumptions for achieving security in various settings, and secure distributed computation.