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Cryptographic hash function

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Because cryptographic hash functions are typically designed to be computed quickly, special key derivation functions that require greater computing resources have been developed that make such brute force attacks more difficult. In some theoretical analyses "difficult" has a specific mathematical meaning, such as "not solvable in asymptotic polynomial time ". Such interpretations of difficulty are important in the study of provably secure cryptographic hash functions but do not usually have a strong connection to practical security.

For example, an exponential time algorithm can sometimes still be fast enough to make a feasible attack. Conversely, a polynomial time algorithm e. An illustration of the potential use of a cryptographic hash is as follows: Alice poses a tough math problem to Bob and claims she has solved it. Bob would like to try it himself, but would yet like to be sure that Alice is not bluffing. Therefore, Alice writes down her solution, computes its hash and tells Bob the hash value whilst keeping the solution secret.

Then, when Bob comes up with the solution himself a few days later, Alice can prove that she had the solution earlier by revealing it and having Bob hash it and check that it matches the hash value given to him before. This is an example of a simple commitment scheme ; in actual practice, Alice and Bob will often be computer programs, and the secret would be something less easily spoofed than a claimed puzzle solution.

An important application of secure hashes is verification of message integrity. Comparing message digests hash digests over the message calculated before, and after, transmission can determine whether any changes have been made to the message or file.

MD5 , SHA1 , or SHA2 hash digests are sometimes published on websites or forums to allow verification of integrity for downloaded files, [7] including files retrieved using file sharing such as mirroring. This practice establishes a chain of trust so long as the hashes are posted on a site authenticated by HTTPS.

Using a cryptographic hash and a chain of trust prevents malicious changes to the file to go undetected. Other error detecting codes such as cyclic redundancy checks only prevent against non-malicious alterations of the file. Almost all digital signature schemes require a cryptographic hash to be calculated over the message. This allows the signature calculation to be performed on the relatively small, statically sized hash digest.

The message is considered authentic if the signature verification succeeds given the signature and recalculated hash digest over the message. So the message integrity property of the cryptographic hash is used to create secure and efficient digital signature schemes. Password verification commonly relies on cryptographic hashes. Storing all user passwords as cleartext can result in a massive security breach if the password file is compromised. One way to reduce this danger is to only store the hash digest of each password.

To authenticate a user, the password presented by the user is hashed and compared with the stored hash. A password reset method is required when password hashing is performed; original passwords cannot be recalculated from the stored hash value. Standard cryptographic hash functions are designed to be computed quickly, and, as a result, it is possible to try guessed passwords at high rates.

Common graphics processing units can try billions of possible passwords each second. Password hash functions that perform Key stretching - such as PBKDF2 , scrypt or Argon2 - commonly use repeated invocations of a cryptographic hash to increase the time and in some cases computer memory required to perform brute force attacks on stored password hash digests. A password hash requires the use of a large random, non-secret salt value which can be stored with the password hash.

The salt randomizes the output of the password hash, making it impossible for an adversary to store tables of passwords and precomputed hash values to which the password hash digest can be compared. The output of a password hash function can also be used as a cryptographic key.

A proof-of-work system or protocol, or function is an economic measure to deter denial-of-service attacks and other service abuses such as spam on a network by requiring some work from the service requester, usually meaning processing time by a computer. A key feature of these schemes is their asymmetry: One popular system — used in Bitcoin mining and Hashcash — uses partial hash inversions to prove that work was done, to unlock a mining reward in Bitcoin and as a good-will token to send an e-mail in Hashcash.

The sender is required to find a message whose hash value begins with a number of zero bits. The average work that sender needs to perform in order to find a valid message is exponential in the number of zero bits required in the hash value, while the recipient can verify the validity of the message by executing a single hash function.

For instance, in Hashcash, a sender is asked to generate a header whose bit SHA-1 hash value has the first 20 bits as zeros. The sender will on average have to try 2 19 times to find a valid header. A message digest can also serve as a means of reliably identifying a file; several source code management systems, including Git , Mercurial and Monotone , use the sha1sum of various types of content file content, directory trees, ancestry information, etc.

Hashes are used to identify files on peer-to-peer filesharing networks. For example, in an ed2k link , an MD4 -variant hash is combined with the file size, providing sufficient information for locating file sources, downloading the file and verifying its contents. Magnet links are another example. Such file hashes are often the top hash of a hash list or a hash tree which allows for additional benefits. One of the main applications of a hash function is to allow the fast look-up of a data in a hash table.

Being hash functions of a particular kind, cryptographic hash functions lend themselves well to this application too. However, compared with standard hash functions, cryptographic hash functions tend to be much more expensive computationally. For this reason, they tend to be used in contexts where it is necessary for users to protect themselves against the possibility of forgery the creation of data with the same digest as the expected data by potentially malicious participants.

There are several methods to use a block cipher to build a cryptographic hash function, specifically a one-way compression function. The methods resemble the block cipher modes of operation usually used for encryption. Many well-known hash functions, including MD4 , MD5 , SHA-1 and SHA-2 are built from block-cipher-like components designed for the purpose, with feedback to ensure that the resulting function is not invertible. SHA-3 finalists included functions with block-cipher-like components e.

A standard block cipher such as AES can be used in place of these custom block ciphers; that might be useful when an embedded system needs to implement both encryption and hashing with minimal code size or hardware area. However, that approach can have costs in efficiency and security. The ciphers in hash functions are built for hashing: General-purpose ciphers tend to have different design goals.

In particular, AES has key and block sizes that make it nontrivial to use to generate long hash values; AES encryption becomes less efficient when the key changes each block; and related-key attacks make it potentially less secure for use in a hash function than for encryption.

A hash function must be able to process an arbitrary-length message into a fixed-length output. This can be achieved by breaking the input up into a series of equal-sized blocks, and operating on them in sequence using a one-way compression function. The compression function can either be specially designed for hashing or be built from a block cipher. The last block processed should also be unambiguously length padded ; this is crucial to the security of this construction.

This design causes many inherent flaws, including length-extension , multicollisions, [8] long message attacks, [9] generate-and-paste attacks, [ citation needed ] and also cannot be parallelized. Hash functions can be used to build other cryptographic primitives.

For these other primitives to be cryptographically secure, care must be taken to build them correctly. Message authentication codes MACs also called keyed hash functions are often built from hash functions. Just as block ciphers can be used to build hash functions, hash functions can be used to build block ciphers. Luby-Rackoff constructions using hash functions can be provably secure if the underlying hash function is secure.

That cipher can also be used in a conventional mode of operation, without the same security guarantees. Pseudorandom number generators PRNGs can be built using hash functions. This is done by combining a secret random seed with a counter and hashing it. Often this is done by first building a cryptographically secure pseudorandom number generator and then using its stream of random bytes as keystream. SEAL is a stream cipher that uses SHA-1 to generate internal tables, which are then used in a keystream generator more or less unrelated to the hash algorithm.

Concatenating outputs from multiple hash functions provides collision resistance as good as the strongest of the algorithms included in the concatenated result. The additional work needed to find the SHA-1 collision beyond the exponential birthday search requires only polynomial time.

There are many cryptographic hash algorithms; this section lists a few algorithms that are referenced relatively often.

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Magnet links are another example. Collisions against MD5 can be calculated within seconds which makes the algorithm unsuitable for most use cases where a cryptographic hash is required.

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The methods resemble the block cipher modes of operation usually used for encryption.

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