Merkle–Damgård construction
method of building collision-resistant cryptographic hash functions
In cryptography, the Merkle–Damgård construction or Merkle–Damgård hash function is a method of building collision-resistant cryptographic hash functions from collision-resistant one-way compression functions. This construction was used in the design of many popular hash algorithms such as MD5, SHA-1, and SHA-2.
The Merkle–Damgård construction was described in Ralph Merkle's Ph.D. thesis in 1979. Ralph Merkle and Ivan Damgård independently proved that the structure is sound: that is, if an appropriate padding scheme is used and the compression function is collision-resistant, then the hash function will also be collision-resistant.
The Merkle–Damgård hash function first applies an MD-compliant padding function to create an input whose size is a multiple of a fixed number (e.g. 512 or 1024) — this is because compression functions cannot handle inputs of arbitrary size. The hash function then breaks the result into blocks of fixed size, and processes them one at a time with the compression function, each time combining a block of the input with the output of the previous round. In order to make the construction secure, Merkle and Damgård proposed that messages be padded with a padding that encodes the length of the original message. This is called length padding or Merkle–Damgård strengthening.
In the diagram, the one-way compression function is denoted by f, and transforms two fixed length inputs to an output of the same size as one of the inputs.
The public source identifies “Merkle–Damgård construction” as method of building collision-resistant cryptographic hash functions. This brief keeps that definition visible, then builds a research path around Merkle, Damgård and construction.
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This entry incorporates text from “Merkle–Damgård construction” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.