"The Theory and Challenges of Cryptography" seminar by Professor Charlie Rackoff
People have been doing cryptography in one form or another for thousands of years, but it is only relatively recently that we have understood the issues involved. For most of the cryptographic tasks we wish to do, the possibility of performing them securely relies on deep assumptions about computational complexity that we are currently unable to prove. With appropriate assumptions, there are some amazing things we can do. If our assumptions are false, however, then just about everything we do on the internet is completely insecure.
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