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In the first category are those functions whose designs are based on mathematical problems, and whose security thus follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called provably secure cryptographic hash functions. To construct these is very difficult, and few examples have been introduced.
It is of interest as a type of post-quantum cryptography. So far, hash-based cryptography is used to construct digital signatures schemes such as the Merkle signature scheme, zero knowledge and computationally integrity proofs, such as the zk-STARK [1] proof system and range proofs over issued credentials via the HashWires [2] protocol.
In cryptography, the fast syndrome-based hash functions (FSB) are a family of cryptographic hash functions introduced in 2003 by Daniel Augot, Matthieu Finiasz, and Nicolas Sendrier. [1] Unlike most other cryptographic hash functions in use today, FSB can to a certain extent be proven to be secure.
hash HAS-160: 160 bits hash HAVAL: 128 to 256 bits hash JH: 224 to 512 bits hash LSH [19] 256 to 512 bits wide-pipe Merkle–Damgård construction: MD2: 128 bits hash MD4: 128 bits hash MD5: 128 bits Merkle–Damgård construction: MD6: up to 512 bits Merkle tree NLFSR (it is also a keyed hash function) RadioGatún: arbitrary ideal mangling ...
The weaker assumption is always preferred in theoretical cryptography, but in practice, a hash-function that is only second pre-image resistant is considered insecure and is therefore not recommended for real applications. Informally, these properties mean that a malicious adversary cannot replace or modify the input data without changing its ...
In cryptography, the avalanche effect is the desirable property of cryptographic algorithms, typically block ciphers [1] and cryptographic hash functions, wherein if an input is changed slightly (for example, flipping a single bit), the output changes significantly (e.g., half the output bits flip).
Let H be a cryptographic hash function and let an output y be given. Let it be required to find z such that H( z) = y. Let us also assume that a part of the string z, say k, is known. Then, the problem of determining z boils down to finding x that should be concatenated with k to get z. The problem of determining x can be thought of a puzzle.
Besides solving the Summation Polynomial Problem, there exists another way how to find second pre-images and thus collisions, Wagner's generalized birthday attack. ECOH is a good example of hash function that is based on mathematical functions (with the provable security approach) rather than on classical ad hoc mixing of bits to obtain the hash.