Cryptographic Hash Functions

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Presentation transcript:

Cryptographic Hash Functions CS 465 Cryptographic Hash Functions Last Updated: Sep 19, 2017

Message Digests Input to a hash function is called a pre-image Output of a hash function is a message digest d, also known as hash codes or hash values Sort of like a message fingerprint/footprint Cryptographic hash functions are ONE-way They cannot be inverted

Properties of a Hash Function (H) H can be applied to a block of data of any size H produces a fixed-length output H(x) is relatively easy to compute for any given x For any given value h, it is computationally infeasible to find x such that H(x) = h For any given block x, it is computationally infeasible to find y ≠ x with H(y) = H(x) It is computationally infeasible to find any pair (x, y) such that H(x) = H(y) (one-way) (weak collision resistance) (strong collision resistance)

Attacks on Hash Functions First pre-image attack Given a digest d, find a message m such that H(m) = d Think property #4 Second pre-image attack Given a message m1, find a different message m2 such that H(m2) = H(m1) Cost: 2n where n = # of digest bits Think property #5 Collisions Two messages both hash to the same value Birthday Attack Given n-bit digest, birthday attack says that we’ll find a match after 2n/2 attempts Think property #6 253 people in a room Odds are good that one of them shares a birthday with you 23 people in a room Odds are good that two people share a birthday

Useful Applications of Hashes Human-readable method to compare/verify data File downloads Before learning suite, we used to have students email in a hash of their projects Chaining events together – blockchain (think Bitcoin) Digital signatures and message authentication codes Fundamental building block of many secure protocols Schneier (Secrets and Lies) – “They are probably the single most useful tool in a cryptographer’s toolbox”

SHA-1 Hash Function The following diagrams illustrates how SHA-1 is implemented SHA-1 is implemented using the Merkle-Damgård construction See http://en.wikipedia.org/wiki/Merkle–Damgård_construction It is important to understand the details of this implementation in order to understand the MAC attack discussed later and the MAC attack lab

Merkle-Damgård Construction

64 bits

MAC attack regions of interest 64 bits MAC attack regions of interest

MD5 and SHA MD5 SHA-0 SHA-1 SHA-2 SHA-3 Completely broken – collisions found SHA-0 SHA-1 Weaknesses discovered, not recommended for new apps after 2010 SHA-2 ok to use, no known flaws SHA-3 Subset of Keccak (pronounce ketchak) New government standard in 2015 based on a competition (like AES) Completely different construction than prior SHA variants Does not use Merkle-Damgard construction – uses a sponge construction A defense in the event that SHA2 collapses See https://en.wikipedia.org/wiki/SHA-3 comparison chart

Lecture Notes See articles about SHA-1 collsions 2005 – Chinese researchers discovered first SHA-1 collisions faster than brute force (2^69) 2017 – Google can generate pdf files with the same SHA-1 hash 100,000 times faster than brute force