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Learn about groundbreaking advances in fully homomorphic encryption (FHE) through this 16-minute conference presentation that introduces novel algorithms for ranking, order statistics, and sorting operations under the CKKS encryption scheme. Discover how researchers from the University of Twente, Linksight, and Carl von Ossietzky Universität Oldenburg have revolutionized privacy-preserving computations by moving away from traditional swap-based techniques to achieve unprecedented efficiency in encrypted data operations. Explore the fundamental challenges of performing comparisons on encrypted data and understand how the new approach leverages SIMD capabilities to enable simultaneous comparisons of all elements, reducing comparison depth to a constant value of up to 2. Examine the technical innovation of homomorphic re-encoding that allows for highly parallelizable operations suitable for hardware acceleration, requiring only O(log N) rotations with minimal computational overhead. Analyze experimental results demonstrating practical performance improvements, including ranking a 128-element vector in 5.76 seconds, computing argmin/argmax in 12.83 seconds, and sorting in 78.64 seconds. Understand the significant implications for cloud computing environments where privacy-preserving database queries and encrypted data processing are essential, and learn how this research advances the state-of-the-art beyond previous solutions that achieved comparison depths of log²N and k log k²N.
