A blog series exploring encrypted search, Bernoulli models, cipher types, and probabilistic data structures
This series explores the mathematical foundations of computing on encrypted and approximate data—where we deliberately trade exactness for privacy, space efficiency, or computational tractability.
The fundamental insight: distinguish between latent (true) values and observed (approximate) values. This duality connects:
A type-theoretic framework for approximate computing:
Category-theoretic foundations for encrypted computation:
Moving beyond computational hardness assumptions:
In an era where:
…these foundations provide principled ways to build systems that trade exactness for other desirable properties while maintaining formal guarantees.
This work builds on research spanning from my Master’s thesis (2015) on encrypted search through recent work on algebraic cipher types and entropy maps. The combination of Bernoulli types with categorical abstractions finally provides a unified mathematical foundation for practical privacy-preserving computation at scale.
Bernoulli data type
Explore project →Published IEEE paper on using bootstrap methods to estimate encrypted search confidentiality against frequency attacks.
A conceptual introduction to entropy maps—implementing functions with hash functions and prefix-free codes.
Introducing Bernoulli types as a unified type-theoretic foundation for probabilistic data structures, approximate computing, and oblivious computation with information-theoretic privacy guarantees.
Using category theory to formalize oblivious computing through cipher maps and algebraic cipher types, enabling functorial composition of privacy-preserving transformations.
Rethinking encrypted search through oblivious types that provide information-theoretic privacy guarantees against access pattern leakage, without relying on computational hardness assumptions.
A functorial framework that lifts algebraic structures into the encrypted domain, enabling secure computation that preserves mathematical properties.
Entropy maps use prefix-free hash codes to map domain values to codomain values without storing the domain, enabling lossy compression with information-theoretic bounds.
Analysis of known plaintext attack vulnerabilities in time series encryption schemes.
Analyzing the space bounds, entropy requirements, and cryptographic security properties of perfect hash functions.
A Boolean algebra framework over trapdoors for cryptographic operations. Introduces a homomorphism from powerset Boolean algebra to n-bit strings via cryptographic hash functions, enabling secure computations with one-way properties.
This blog post introduces the Bernoulli Model, a framework for understanding probabilistic data structures and incorporating uncertainty into data types, particularly Boolean values. It highlights the model's utility in optimizing space and accuracy in data representation.
A C++ library for composable hash functions using algebraic structure over XOR, with template metaprogramming.
Exploring rank-ordered search over encrypted documents using oblivious entropy maps, enabling relevance scoring without revealing document contents.
Three Python approximations of a random oracle, each illuminating a different tradeoff between true randomness, determinism, and composability.
An exploration of Bloom filters as elegant probabilistic data structures that trade perfect recall for extraordinary space efficiency.