World Library  
Flag as Inappropriate
Email this Article

Collision resistance

Article Id: WHEBN0002982326
Reproduction Date:

Title: Collision resistance  
Author: World Heritage Encyclopedia
Language: English
Subject: Very smooth hash, Merkle–Damgård construction, File verification, Passwd, Symmetric-key cryptography
Collection: Symmetric-Key Cryptography, Theory of Cryptography
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Collision resistance

Collision resistance is a property of cryptographic hash functions: a hash function H is collision resistant if it is hard to find two inputs that hash to the same output; that is, two inputs a and b such that H(a) = H(b), and ab.[1]:136

Every hash function with more inputs than outputs will necessarily have collisions.[1]:136Consider a hash function such as SHA-256 that produces 256 bits of output from an arbitrarily large input. Since it must generate one of 2256 outputs for each member of a much larger set of inputs, the pigeonhole principle guarantees that some inputs will hash to the same output. Collision resistance doesn't mean that no collisions exist; simply that they are hard to find.[1]:143

The "birthday paradox" places an upper bound on collision resistance: if a hash function produces N bits of output, an attacker who computes only 2N/2 (or \scriptstyle \sqrt{ 2^N}) hash operations on random input is likely to find two matching outputs. If there is an easier method than this brute-force attack, it is typically considered a flaw in the hash function.[2]

Cryptographic hash functions are usually designed to be collision resistant. But many hash functions that were once thought to be collision resistant were later broken. MD5 and SHA-1 in particular both have published techniques more efficient than brute force for finding collisions.[3][4] However, some hash functions have a proof that finding collisions is at least as difficult as some hard mathematical problem (such as integer factorization or discrete logarithm). Those functions are called provably secure.[2]

Rationale

Collision resistance is desirable for several reasons.

  • In some digital signature systems, a party attests to a document by publishing a public key signature on a hash of the document. If it is possible to produce two documents with the same hash, an attacker could get a party to attest to one, and then claim that the party had attested to the other.
  • In some proof-of-work systems, users provide hash collisions as proof that they have performed a certain amount of computation to find them. If there is an easier way to find collisions than brute force, users can cheat the system.
  • In some distributed content systems, parties compare cryptographic hashes of files in order to make sure they have the same version. An attacker who could produce two files with the same hash could trick users into believing they had the same version of a file when they in fact did not.

See also

References

  1. ^ a b c Goldwasser, S. and Bellare, M. "Lecture Notes on Cryptography". Summer course on cryptography, MIT, 1996-2001
  2. ^ a b Pass, R. "Lecture 21: Collision-Resistant Hash Functions and General Digital Signature Scheme". Course on Cryptography, Cornell University, 2009
  3. ^ Xiaoyun Wang and Hongbo Yu. "How to Break MD5 and Other Hash Functions" (PDF). Retrieved 2009-12-21. 
  4. ^ Xiaoyun Wang, Yiquin Lisa Yin, Hongobo Yu. "Finding Collisions in the Full SHA-1" (PDF). 
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.