Hash function algorithms

Hash Function Algorithms. Hash function algorithms are not considered actual encryption, although they are often used with encryption algorithms. Hash functions are used to verify passwords or digital signatures, to look up a file or a table of data, to store data, to verify e-mail users, to verify... 

SHA-1 (secure hashing algorithm) is a NIST-sponsored hashing function that has been... 

One may want the hash function to reduce the message length by more than the 1 or 2 bits required above. Hence let a monotonically increasing function /e o be given, which is to be approximated by len from below. A polynomial-time algorithm that computes len in unary and a value g N are also needed such that for all k >... 

The function len is defined by len k ) = length make small(k )), as explained above, and the polynomial-time algorithm that computes it in unary is the composition of those for length and make small. The value that denotes from where on the hash functions are length-reducing is ki . 

Remark 8.54. This family of hash functions can be augmented by short collision proofs according to Remark 8.37 The reduction used in the proof of the theorem yields a (rather obvious) algorithm to construct a collision of the underlying family of fixed-size hash functions, from any collision of the new family (for all acceptable keys, although it is only needed for correctly generated keys in the proof of collision-intractability). ... 

As the construction of hash functions was in several steps, it may be useful to summarize the result for the concrete case of subgroups of prime fields, as in Definition 8.21 and Construction 8.22, and to study how the parameters should be chosen. In particular, the algorithm gen is considered variable, i.e., the relation between the lengths of q and p, and the function make small. 

For SigScheme, an algorithm A is defined that uses A and simulates the actions of the risk bearer s entity with respect to the family of hash functions on its own. Thus, on input ( 1 , V, prek), it computes k° = make small(k) K° <— gen°CV ) prek = prek, K°) proof A CV , "V, prek ). If proof contains a component procf, A outputs that. In Case 1, this immediately yields a contradiction to the security for the risk bearer in SigScheme. 

This necessity mainly has to do with the numerous applications that do not call for high throughput implementations (as long as the security part is concerned) but for small-sized or low-power implementations. In these cases the usage of CMAC instead of HMAC is ideal since there is no need to incorporate both a hash function and a cipher block but only a block cipher algorithm like AES (NIST, 2001 a) that can handle all asp>ects of security in the certain security scheme. 

Symmetric key cryptography uses a polyalpha-betic encryption algorithm, such as a block cipher, a stream cipher, or a hash function to convert the data into binary code. A block cipher apphes the same key to each block of data. Stream ciphers encrypt the data bit by bit. They can operate in several ways, but two common methods are self-synchronizing and synchronous. The self-synchronizing cipher encrypts the data bit by bit, using an algebraic function applied to the previous bit. Synchronous ciphers apply a succession of functions independent of the data. 

One of the most commonly used hash algorithm employs twin prime numbers (two consecutive odd numbers that are both primes) and modulo function. If KEY is a large number (fragment ID or XOR-ed parts of chopped long string) and NP the length of the direct access file than the calculated address ADDR and the increment INCR can be obtained by the following equations ... 

A hash algorithm is a basic technique in asymmetric cryptography it is an irreversible mathematical function that yields a certain value when used with a data file. For example, used with a document it always yields the same value but it is impossible to calculate the document from the hash value. 

A function len N N, called the length function (denoting the length of the hash values in terms of the security parameter), and a polynomial-time algorithm that computes len in unary. 

A polynomial-time algorithm hash that computes the whole family of functions, i.e., on input K e All and a bit string m, it outputs the hash value hashj m). 

---