# Hash Functions Are Just Mathematical Algorithms Computer Science Essay

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In addition to the ciphers, another important encryption technique that is often incorporated into cryptosystems is the HASH FUNCTION. The HASH FUNCTIONS are just the mathematical algorithms that generate a message summary or digest (sometimes called the Finger Print) to confirm the identity of a specific message and to confirm that there have not been any changes to the content. While they do not create a cipher text, HASH FUNCTIONS confirm message identity and integrity, both of which are critical functions in e-commerce. Hence the HASH FUNCTIONS that are used in cryptography takes in an arbitrary set of data that are in blocks, and gives back a bit string, that is fixed in size. If any change happens to the data, it affects the HASH VALUE in turn. The information or the data that is to be encrypted is usually called the MESSAGE and the HASH VALUE that is used to encrypt the message is known as MESSAGE DIGEST or DIGEST.

The values that are returned by the HASH FUNCTIONS are known as HASH VALUES, HASH CODES, HASH SUMS, CHECK SUMS or just HASHES. The HASH FUNCTIONS are mostly used in a Look Up Table, to compare data in a database. This is used to analyze redundancies in a large file. HASH FUNCTIONS are generally used in HASH TABLES. It is used to generally locate an item in a record using the search key. The HASH FUNTION usually connects the search key and the index. Hence the place is indicated by the index, where the record should be stored. The domain of the HASH FUNCTION is usually larger than its own range. And hence it will connect many search keys to the same index. Thus each of a HASH TABLE is connected with a set of records. Thus each slot of a HASH TABLE is known as a BUCKET. And the HASH VALUES are known as BUCKET INDICES.

Hash Algorithms are also known as public functions that create a HASH VALUE, also known as a message digest, by converting variable-length messages into a fixed-length value. The Message Digest, that is a Fingerprint of the author' message and that is compared with the recipient's locally calculated hash of the same message. HASH FUNCTIONS are considered one-way operations in that the same message always provides the same HASH VALUE, but the HASH VALUE itself cannot be used to determine the contents of the message. The HASH FUNCTIONS do not usually require the use of keys, but it is possible to attach a MESSAGE AUTHENTICATION CODE(MAC), a key-dependent, one-way HASH FUNCTION-that allows only specific recipients to access the Message Digest.

Just because the HASH FUNCTIONS are one-way, they are used in password verification systems to confirm the identity of the user. In such systems, the HASH VALUE or the Message Digest is calculated based upon the originally issued password, and this Message Digest is stored for later comparison. When the user logs on for the next session, the system calculates a HASH VALUE based on the user's password input, and this value is compared against the stored value to confirm identity of the user. In such systems, the HASH VALUE, or Message Digest, is calculated based on the originally issued password and this message digest is stored for later comparison.

When the user logs on for the next session, the system calculates a HASH VALUE based on the user's password input, and this value is compared against the stord value to confirm identity. The HASH FUNCTIONS are also used to construct CACHES for a large set of data. This CACHE is generally simpler than a HASH TABLE to search for an item, since duplications can be discarded.

## DEFINING HASH FUNCTIONS:

The quantity of the usage of electronic communication has also become enormous. This has caused some new issues in the field of Information Security. Thus the methods in cryptography have been very much under observation. There are certain primitives that the recent Cryptographic protocols adopt. One among those is the HASH FUNCTIONS that are used to generate short HASH VALUES the messages that is of any length. The passwords of the users are usually encoded with HASH FUNCTIONS. Information is usually hacked and is not received properly by the receiver. Thus information protection is necessary in a communication; for instance in Digital Signatures. Theoretically, we take into consideration, the KEYED HASH FUNCTION, as in the following expression:

Let l and n be the positive integers. Hash function is depicted by 'f ', which has an output of n-bits. And the l-bit key takes in two inputs, which contains the arbitrary length first and next, of length l bits. And the result is a binary string of length n.

H: {0,1}* {0,1} l {0,1} n

A HASH is generally considered the Unique string of data. The creation of HASH is known as HASHING. The output of the HASH is unique to the original information.

A HASH FUNCTION that is used in cryptography takes in an arbitrary set of data that are in blocks, and gives back a bit string, that is fixed in size. If any change happens to the data, it affects the HASH VALUE in turn. The information or the data that is to be encrypted is usually called the MESSAGE and the HASH VALUE that is used to encrypt the message is known as MESSAGE DIGEST or DIGEST.

The values that are returned by the HASH FUNCTIONS are known as HASH VALUES, HASH CODES, HASH SUMS, CHECK SUMS or just HASHES. The HASH FUNCTIONS are mostly used in a Look Up Table, to compare data in a database. This is used to analyze redundancies in a large file. HASH FUNCTIONS are generally used in HASH TABLES. It is used to generally locate an item in a record using the search key. The HASH FUNTION usually connects the search key and the index. Hence the place is indicated by the index, where the record should be stored. The domain of the HASH FUNCTION is usually larger than its own range. And hence it will connect many search keys to the same index. Thus each of a HASH TABLE is connected with a set of records. Thus each slot of a HASH TABLE is known as a BUCKET. And the HASH VALUES are known as BUCKET INDICES.

Hash Functions may be used to create HASHES. They are Cryptographic Algorithms. In general, Cryptographic Algorithms are often grouped into two broad categories, which are symmetric and asymmetric algorithms. Symmetric and Asymmetric algorithms are distinguished by the types of keys they use for encryption and decryption operations.

There are many common algorithms that are used. Hence such algorithms are MESSAGE DIGEST (MD) and SECURE HASH FUNCTION (SHA).There are several versions that are available for Message Digest. The version which is being used at present is MD5. It is an automatic procedure for Simple Network Management Protocol (SNMP). Researchers figured out Redundancies and collisions in the MD5 program. Hence a more protected Cryptographic algorithm is suggested for HASHING.

Thus SECURED HASH FUNCTIONS (SHA) gives us a longer HASH than many versions of MD that results in a more protected code. According to the recent surveys, there have been no limitations found with the most recent versions of SHA-1 and SHA-2. And yet another version, SHA-3, is yet to be released that was finished developing in 2012.Hence in this report, we will in detail about all the versions of SECURED HASH FUNCTION. The ultimate objective of this research about SHA is to protect the data that is transmitted.

The HASH FUNCTIONS, mostly the SHA-1, which was initially constructed for the use in a handful of cryptographic

## Properties of Hash Functions:

A Cryptographic Hash Function must be resistant of any sort of attack. And hence must possess the following qualities:

## Pre-image resistance:

For a given Hash h, it must be very hard to find any message m such that h=hash (m). This concept in some way relevant to one-way function. Those functions that dearth this quality are prone to pre-image attacks.

## Second pre-image resistance:

On giving an input m1, it must be very hard for us to find any message m, such that hash (m1) = hash (m2). This is at times known as weak collision resistance. Those functions that dearth this quality are prone to second-pre-image attacks.

## Collision resistance:

It must be hard to figure out two distinct messages m1 and m2, such that hash (m1)=hash(m2). Such a duo is called a cryptographic hash collision. This quality is sometimes known as strong collision resistance.

## SECURED HASH ALGORITHMS (SHA):

The Secured Hash Standards(SHS), is a standard issued by the National Institute of Standards and Technology(NIST).Standard document FIPS 180-1 specifies SHA-1 as a secure algorithm for computing a condensed representation of a message or data file.SHA-1 produces a 160-bit message digest, which can be used as an input to a digital signature algorithm. SHA-1 is based on principles modeled after MD4. New hash algorithms have been proposed by NIST as standards for 128, 192 and 256 bits respectively.The number of bits used in the hash algorithm is a measurement of the strength of the algorithm against collision attacks. SHA-256 is essentially a 256-bit block cipher algorithm that creates a key by encrypting the intermediate hash value, with the message block functioning as the key. The compression function operates on each 512-bit message block and a 256-bit intermediate message digest. The various HASH VALUES are:

Data Format Data:

Key Format Key

## Principles of Information Security

## Text String

HMAC

Texting String

MD4

02c749afe3ec08974

41817133e8d9b1

2e74c8afce124deb01563

Fb6cceebac738dd97711

Db6e2c6c28697488ccce13b

21309f28a003c6cc05be

Help

Calculate

Close

## SLAVASOFT

RIPEMD160

MD2

SHA 348

SHA 256

SHA1

In Hash Functions, there are four general SHA algorithms, that are figured differently and are segregated as SHA-0,SHA-1,SHA-2 and SHA-3. SHA-0 and SHA-1 are almost similar except for which the SHA-1 will correct an error in the authentic SHA HASH specifications that has been led to a critical limitation.