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# ChainHash Definitions

## chain variable

A chain variable is a variable taking value in the set of all bit strings of a specified length.

## block

A block is a bit string of a specified length.

## compression function

A compression function is a function from the product space of the domains of a specified set of chain variables and the Set of all blocks of some fixed length to the product space of the domains of the chain variables.

## initial value

An initial value is a explicitly specified point in the product space of the domains of a set of chain variables.

## padding algorithm

A padding algorithm is an algorithm which appends bits to a bit string giving a new bit string whose length has some desired propery.

## chain hash function

A chain hash function is a function constructed from a compression function, padding algorithm and initial value in such a manner as to have the following properties:

- Its domain is either all bits string up to some specified length, or arbitrary length bit strings.
- Its range is the equal to the range of the compression function.
- The value of the function at a bit string is determined as follows:
  - The bit string is padded by using the padding algorithm to increase its length to a multiple of the size of the blocks of the compression function.
  - The chain variables are set equal to the initial value.
  - For each block in the padded message, the chain variables' values are updated to the value of the compression function at the point specified by the chain variable and the block.
  - The value of the chain hash function is equal to the concatenation of the final values of the chain variables.

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