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okay thank you hope you all had a little break and uh its quite uh an excellent talk that john has given its hard to follow him but i will do my best okay so today ill try to tell you how to hide the secrets in software and my name is rachel the fundamental question we are asking here is what is the minimum information that a computer program that we work with every day really needs to give away in order to do its job and when i say computer program you will immediately think about some program written in your favorite computer language maybe python maybe java maybe mala but we know that theoretically all of those can be translated into this mathematical model called arithmetic circuits in some finite field zp and which basically involves a sequence of addition and multiplication in other words every output element is the outcome of evaluating some polynomial on the input variables of course these polynomials are hugely complex and they might have very very high degree for example t