The sponge construction as a source of secure cryptographic primitives

Most of modern cryptography primitives have no provably secure constructions. Their safety is defined on the basis of well-known in the given time cryptanalytic attacks. Moreover, the asymptotic nature of cryptographic definitions (and definitions of complexity theory in general) does not let us say anything about how hard it is to break a given cryptographic primitive for keys of a certain fixed length. Sponge constructions equipped with one ideal permutation and appropriate security parameters are suitable for building provably secure cryptographic primitives. The cryptographic primitives based on sponge and duplex constructions cover most symmetric crypto operations.