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Explore a groundbreaking talk from Eurocrypt 2012 on Fully Homomorphic Encryption with Polylog Overhead, presented by authors Craig Gentry, Shai Halevi, and Nigel P. Smart. Delve into cutting-edge cryptographic research that addresses the challenge of efficient fully homomorphic encryption schemes. Gain insights into the innovative techniques and algorithms proposed to achieve polylogarithmic overhead in homomorphic operations. Understand the potential implications of this research for secure cloud computing, privacy-preserving data analysis, and other applications requiring computation on encrypted data.