MT25 Strachey Lecture - Professor Rafail Ostrovsky: Advances in Garbled Circuits Nearly 40 years ago, Andy Yao proposed the construction of “Garbled Circuits,” which had an enormous impact on the field of secure computation -- both in theory and in practice. In Garbled Circuits, two parties agree on a Boolean circuit that they want to evaluate, where both parties have partial, disjoint inputs to the circuit, and neither party is willing to disclose to the other party anything but the output. In this talk, I will survey the state of the art for garbling schemes, including computing with Garbled Random Access Memory, the so-called GRAM constructions that were invented by Lu and Ostrovsky in 2013, as well as more recent progress, including the GRAM paper by Heath, Kolesnikov and Ostrovsky, which received the best paper award in Eurocrypt 2022. I will also discuss Garbled Circuits in the malicious setting, where parties try to deviate arbitrarily from the prescribed protocol execution to gain additional information, and will review some of the latest advances in this area. The talk will be self-contained and accessible to the general audience.