Probabilistic Data Structures for Software Security

We are living in an era where software systems are growing in size with each passing day and often face a constant tension between the scale, performance, and security, where each of them is essential and non-negotiable. Security tools must process large volumes of data in real time (network logs, user activity, login attempts, password matches, etc.), but storing and analyzing data in traditional formats is slow, expensive, and often impractical. 

Traditional data structures (through databases, logs, hash tables, etc.) aim at providing exact answers for queries like 

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