It's a function that takes an input of any length and produces an output of the requested length.
From the Keccak (SHA-3) authors [1]: A sponge function is a generalization of both hash functions, which have a fixed output length, and stream ciphers, which have a fixed input length. It operates on a finite state by iteratively applying the inner permutation to it, interleaved with the entry of input or the retrieval of output.
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On top of its original goal as a security reference, we realized that the sponge construction could also be used to build efficient cryptographic primitives. An important aspect is that the cryptographic primitive to be designed is a fixed-length permutation rather than harder-to-build structures such as block ciphers or dedicated compression functions. This is rather good news in itself, as all the symmetric cryptographic services can be realized using only a single primitive: a fixed-length permutation. As opposed to a block cipher, a fixed-length permutation makes no distinction between data and key input and hence can treat all input bits on an equal footing and at the same time can be made simpler.
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With its arbitrarily long input and output sizes, the sponge construction allows building various primitives such as a hash function, a stream cipher or a MAC. In some applications the input is short (e.g., a key and a nonce) while the output is long (e.g., a key stream). In other applications, the opposite occurs, where the input is long (e.g., a message to hash) and the output is short (e.g., a digest or a MAC).
From the Keccak (SHA-3) authors [1]: A sponge function is a generalization of both hash functions, which have a fixed output length, and stream ciphers, which have a fixed input length. It operates on a finite state by iteratively applying the inner permutation to it, interleaved with the entry of input or the retrieval of output.
(...)
On top of its original goal as a security reference, we realized that the sponge construction could also be used to build efficient cryptographic primitives. An important aspect is that the cryptographic primitive to be designed is a fixed-length permutation rather than harder-to-build structures such as block ciphers or dedicated compression functions. This is rather good news in itself, as all the symmetric cryptographic services can be realized using only a single primitive: a fixed-length permutation. As opposed to a block cipher, a fixed-length permutation makes no distinction between data and key input and hence can treat all input bits on an equal footing and at the same time can be made simpler.
(...)
With its arbitrarily long input and output sizes, the sponge construction allows building various primitives such as a hash function, a stream cipher or a MAC. In some applications the input is short (e.g., a key and a nonce) while the output is long (e.g., a key stream). In other applications, the opposite occurs, where the input is long (e.g., a message to hash) and the output is short (e.g., a digest or a MAC).
[1] http://sponge.noekeon.org/