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Hash Functions

Algorithms/Data Structures

What are hash functions?

Hash functions are mathematical algorithms that take input data of arbitrary length and convert it into a fixed-size alphanumeric string output called a hash value. They are deterministic functions that always produce the same hash for a given input.

Hash functions exhibit useful one-way properties where it is easy to compute hashes but difficult to reconstruct the input from a hash. Cryptographic hash functions have additional collision resistance properties.

These characteristics make hash functions ideal for efficiently mapping data to compact fixed-size representations as used in specialized data structures like Count Min Sketches for analytics techniques such as data pruning.

What do they do/how do they work?

Hash functions apply compression functions and logic designed to generate seemingly random hash distributions from any input data. The same input always returns the same hash output. Small changes in input produce significantly different hashes due to avalanche effects.

Common classes of hash functions include cyclic redundancy checks (CRC), checksums, message digests like MD5, and cryptographic hashes like SHA-256. Their inner workings vary based on design tradeoffs.

Why are they important? Where are they used?

Hash functions enable fast lookups, data integrity checks, data structures like hash tables and bloom filters, message authentication codes (MACs), digital fingerprints, cryptocurrencies, and database indexing.

Applications rely on their efficiency, deterministic nature, diffusive properties and in some cases cryptographic collision resistance for security and data management.

FAQ

What are the types of hash functions?

Main categories of hash functions based on properties and use cases:

  • Checksums: Quick error detection like in data transmission
  • Cryptographic: Collision resistant, one-way like SHA-256
  • Message digests: Data fingerprinting like MD5
  • Bloom filters: Space efficient set membership
  • Locality-sensitive: Similar inputs hash alike like SimHash

    • What are the desired properties of a hash function?

    Ideal hash functions have a combination of useful properties:

  • Deterministic - Same input gives same hash
  • Uniform distribution - Outputs seem random
  • One-way function - Hard to invert
  • Collision resistant - Difficult to make inputs with same hash
  • Avalanche effect - Small input changes affect output significantly

    • What are common hash function applications?

    Hash functions have many applications including:

  • Data integrity checks like file checksums
  • Database indexing and hash tables
  • Digital signatures and blockchain ledgers
  • Message authentication codes and challenge-response authentication
  • Data deduplication and caching
  • Cryptography like password hashing

    • What are challenges with hash functions?

    Hash functions come with tradeoffs and challenges around:

  • Collision attacks breaking one-wayness and collision resistance
  • Rainbow table attacks on common hashes
  • Vulnerabilities to length extension and partial preimage attacks
  • Finding balanced hash functions with minimal collisions
  • Needing extra defenses like salting against various attacks

    • References:

  • [Book] Designing Data-Intensive Applications
  • [Article] A Survey on Transactional Stream Processing
  • [Article] The Dataflow Model: A Practical Approach to Balancing Correctness, Latency, and Cost in Massive-Scale, Unbounded, Out-of-Order Data Processing
  • [Post] Sliding Window Hash Join: Efficiently Joining Infinite Streams with Order Preservation
  • [Post] General-purpose Stream Joins via Pruning Symmetric Hash Joins

    • Related Topics

    Data Pruning

    Data pruning refers to database techniques that eliminate irrelevant data during query processing to minimize resource usage and improve performance.

    Count Min Sketch

    A Count Min Sketch is a probabilistic data structure used to estimate item frequencies and counts in data streams.

    Collision Resistance

    Collision resistance is the property of cryptographic hash functions to minimize chances of different inputs mapping to the same output hash, making it difficult to intentionally cause collisions.

    Probabilistic Data Structures

    Probabilistic data structures are space and time efficient data structures that use randomized algorithms to provide approximate results to queries with strong guarantees.

    Distributed Hash Table

    A distributed hash table (DHT) is a decentralized distributed system that partitions a key space across nodes and uses hash functions to assign ownership and locate data.

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